A wire is suspended vertically from a rigid support. When loaded with a steel weight in air, the wire extends by 16 cm. When the weight is completely immersed in water, the extension is reduced to 14 cm. The relative density of the material of the weight is
The surface tension of a soap solution is 2 × 10 − 2 N / m . To blow a bubble of radius 1 cm, the work done is
If T is the surface tension of soap solution, the amount of work done in blowing a soap bubble from a diameter D to 2D is
Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies before and after the change is
The excess of pressure inside a soap bubble than that of the outer pressure is
Water rises upto 10 cm height in a long capillary tube. If this tube is immersed in water so that the height above the water surface is only 8 cm, then
An ideal fluid flows through a pipe of circular cross section made of two sections with diameter 2.5 cm and 3.75 cm. The ratio of the velocities in the two pipes is
A wooden cube of side length 1m and mass 600 kg is floating in water. Then hydrostatic pressure on the bottom surface of the cube is
A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be
A hollow cylinder of mass m made heavy at its bottom is floating vertically in water. It is tilted from its vertical position through an angle θ and is left. The respecting force acting on it is
If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake?
solid ball made of material having coefficient of volume expansion 8 × 10 – 6 / C o is immersed in a Liquid having coefficient of volume expansion 3 × 10 – 6 / C o . The percentage change in upthrust when temperature is increased by 100°C is :
Select the wrong statement. when a body of density ρ and volume V is floating in a liquid of density ρ I
A small solid ball is dropped from a height above the free surface of a liquid. It strikes the surface of the liquid at t = 0. The density of the material of the ball is 500 kg/ m 3 and that of liquid is 1000 kg/ m 3 . If the ball comes momentarily at rest at t = 2 sec then initial height of the ball from surface of liquid was (neglect viscosity):
At which of the following temperatures, the value of surface tension of water is minimum
Soap helps in cleaning clothes, because
The surface tension of soap solution is 25 × 10 − 3 Nm − 1 . The excess pressure inside a soap bubble of diameter 1 cm is
A soap bubble in vacuum has a radius of 3 cm and another soap bubble in vacuum has a radius of 4 cm. If the two bubbles coalesce under isothermal condition, then the radius of the new bubble is
If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake
A metal block of base area 0 . 2 m 2 is connected to a 0.02 kg mass via a string that passes over an ideal pulley as shown in figure. A liquid film of thickness 0.6 mm is placed between the block and the table. When released the block moves to the right with a constant speed of 0.17 m/s. The co-efficient of viscosity of the liquid is :
The maximum speed of flow of water through a long cylindrical pipe of diameter 2cms so that the flow remains laminar is [ given that coefficient of viscosity of water η = 10 − 3 pa − s ]
By a surface of a liquid we mean
A cubical block of wood of side 10 cm floats at the interface between an oil and water with its lower surface 2 cm below the interface. The heights of the oil and water columns are 10 cm each. Density of oil is 0.8g/c.c. The mass of the block is
E is surface energy of a liquid drop. If this drop is sprayed into 64 identical drops, the surface energy of all those drops is
A pipe line of diameter 5 cm is connected to a nozzle whose outlet diameter is 1 cm. If water is flowing in the pipe line with a speed of 0.5 m/s, with what speed is water coming out of the nozzle?
A water barrel stands on a table of height h. If a small hole is punched in the side of the barrel at its base, it is found that the resultant stream of water strikes the ground at a horizontal distance R from the table. What is the depth of water in the barrel?
A hemispherical bowl just floats without sinking in a liquid of density 1 . 2 × 10 3 kg / m 3 . If outer diameter and the density of the bowl are I m and 2 x l 0 4 kg / m 3 respectively, then the inner diameter of the bowl will be
A long cylindrical tank of radius I m is being filled by a pipe of radius 2 cm. The incoming water has a velocity of l m/s. The tank has a hole of radius l cm at the bottom. What is the height of water in the tank in steady state?
Iceberg floats in sea water with a part of it submerged. The percentage fraction of the ice berg submerged is (Density of ice : 0.9 g cm – 3 , density of sea water : I . I g cm – 3 )
The cylindrical tube of a spray pump has a cross-section of 6 cm 2 one of which has 50 holes each of diameter I mm. If the liquid flow inside the tube is 1.2 m per minute, then the speed of ejection of the liquid through the holes is
An ice cube containing a piece of lead floats in water. What would be the effect on the level of water if the ice cube melts?
A metallic sphere floats in an immiscible mixture of water (p w = 10 3 kg/m 3 ) and a liquid (p 1 = 13.5 x 10 3 kg/m 3 ) such that its 1 5 th portion is in water and portion is in liquid. Density of the metal is:
An object is made of a material of density 0.4 gm/cc. It is held 12 cm above the surface of water contained in a vessel and released. The depth it touches in water is :
A concrete sphere of radius R has a cavity of a radius r which is packed with sawdust. Specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water.Ratio of mass of concrete to mass of sawdust will be :
Consider the following statements (A) In the steady flow of an ideal fluid, the velocity at any point is same for different fluid particles. (B) Steady fluid flow is an unaccelerated fluid flow. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) In taking into account the fact that any object which floats must have an average density less than that of water during world war I, a number of cargo vessels are made of concrete. (B) Concrete cargo vessels were filled with air. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) In the three cases shown in the figure, force exerted by liquid on the bottom of vessels is same. (B) Pressure at the bottom in each case is same. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) For a floating body to be in stable equilibrium, its centre of buoyancy must be located above the centre of gravity. (B) The torque produced by the weight of the body and the upthurst will restore body back to its normal position, after the body is disturbed. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) When two boats sail parallel in the same direction and close to each other, they are pulled towards each other. (B) When the boats are close to each other, the velocity of water between them increases and pressure falls according to Bernoulli’s theorem. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
An L-shaped glass tube is immersed in a flowing liquid such that its opening is pointing against the currents. If the speed of flow is v, Study following statement: (i) The liquid in the tube rises to a level A (ii) The liquid in the tube rises to the level B (iii) The liquid in the tube rises to the level C (iv) The magnitude of h is v 2 2 g Choose the correct statement(s).
A man is rowing a boat of mass m with a constant velocity ‘ v 0 ‘ in a river the contact area of boat is ‘A’ and coefficient of viscosity is η . The depth of river is ‘D’. Assume that velocity gradient is constant. The force required to row the boat is
A copper sphere is dipped into water. Which of the following will be true?
A U-tube contains two immiscible non-reacting liquids. P A , P B , P C and P D are pressures at points A, B, C and D respectively. Then
A cylindrical container of cross-sectional area 2 m 2 is partially filled by water. A wooden block of mass 2 kg is gently placed on the free surface of water. Then increase in pressure on the bottom of the container is [density of wood is 0.85 gm/cm 3 ]
A body is floating in water in stable equilibrium. If G be its centre of gravity, B is the centre of buoyancy and M be its metacentre, then
When a large drop of mercury is gently placed on Q horizontal glass surface, which of the following figure correctly shows its shape?
Three soap bubbles A, B and C are formed at the opened ends of a T-shaped pepe. S is a stop cock and initially it is closed. Bubbles B and C are same in size and A has the smallest radius. Then after S is opened
The tube shown in figure contains two immiscible non reacting liquids of densities ρ and 2 ρ . If length l of column of liquid of density ρ is 16 cm, find the difference h between the free surfaces of the liquids in the two arms
The lower end of a vertical glass capillary tube of radius 2r is dipped in water. Now a solid glass rod of radius r is coaxially inserted into the tube. It surface tension of water is T and density of water is ρ , then capillary rise (h) is
When a drop of water is dropped on oil surface, then
If work done in increasing the size of a soap film from 10 c m × 6 c m to 10 c m × 11 c m is 2 × 10 − 4 J , then the surface tension is
A mercury drop of radius 1cm is sprayed into 10 6 drops of equal size. The energy expended in joules is (surface tension of Mercury is 460 × 10 − 3 N / m )
Nature of meniscus for liquid of 0 o angle of contact
The excess pressure due to surface tension in a spherical liquid drop of radius r is directly proportional to
When the temperature is increased the angle of contact of a liquid
For which of the two pairs, the angle of contact is same
A capillary tube of radius r is dipped in a liquid of density ρ and surface tension S. If the angle of contact is θ , the pressure difference between the two surfaces in the beaker and the capillary
The excess of pressure across a soap bubble of radius r is p = 4 T / r . where T is surface tension of soap solution. What is the excess of pressure across an air bubble of the same radius r formed inside a container of soap solution ?
A plumb line is suspended from the ceiling of a car moving with horizontal acceleration of a. What will be the angle of inclination with vertical?
Due to constant leakage of water from the tank shown in figure, water level is lowering with a speed of u. The hole area is A and the cross sectional area of the tank is 10A. What will be the range of water stream on the horizontal ground ? Given that u = 4cm/sec
Consider a solid sphere of radius R and mass density ρ r = ρ 0 1 − r 2 R 2 , 0 < r ≤ R . The minimum density of a liquid in which it will float is:
Two liquids of densities ρ 1 and ρ 2 ρ 2 = 2 ρ 1 are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):
A cylindrical container of cross sectional area A is filled with water. There is a small orifice at the bottom of the container and cross sectional area of the orifice is ‘a’ = nA (n < 1). When depth of water in the container is 0.8 m, the velocity of water emerging from the orifice is (Take g = 10 m / s 2 )
A metal plate of area 2 m 2 is pulled horizontally with a velocity of 0.5 m/s on a 1 mm thick liquid layer. If the viscosity of liquid is 1.2 N − s / m 2 , the force required to pull the plate is
Speeds of air blow on the upper and lower surfaces of a wing of an aeroplane are V 1 a n d V 2 respectively. If A be the cross sectional area of the wing and ρ be the density of air, then the upward lift is
A wooden cube of length 10 cm is floating in water with 75% of its length submerged in water. Now a small disc of iron is placed on the cube and it is observed that the cube is just submerged in water. Then mass of the disc is
The spring balance A read 2 k.g. with block of mass m suspended from it. A balance B reads 5kg. when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in flg. In this situation.
A disc of paper of radius R has a hole of radius r. It is floating on a liquid of surface tension T. The force of surface tension of the disc is
If a vessel containing a fluid of density ρ upto height h is accelerated vertically downwards with acceleration a o then the pressure by fluid at the bottom of vessel is: (Atmosphere pressure = P 0 )
A water tank which is on ground has an arrangement to maintain a constant water level of depth 60 cm. Through a hole on its vertical wall at a depth of 20cm from the free surface water comes out and reaches the ground at a certain distance. To have the same horizontal range another hole can be made at a depth of
Two small spherical metal balls, having equal masses, are made from materials of densities ρ 1 and ρ 2 (ρ 1 = 8ρ 2 ) and have radii of 1mm and 2mm, respectively. They are made to fall vertically (fromrest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1ρ 2 . The ratio of their terminal velocities would be
Considering the pressure ‘P’ to be proportional to the density of air ‘d’, the pressure at height ‘h’ if the pressure on surface of earth is ‘P 0 ’ and density ‘d 0 ’, under isothermal conditions
An air bubble of radius 1cm rises from the bot-tom portion through a liquid of density 1.5g/cc at constant speed of 0.25cm/s. If the density of air is neglected the coefficient of viscosity of the liquid is approximately (In pa. s)
The rate of steady volume flow of water through a capillary tube of length 'l' and radius 'r' under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)
Two capillary tubes of lengths in the ratio 2:1 and radii in the ratio 1:2 are connected in series. Assume the flow of the liquid through the tube is steady. Then, the ratio of pressure difference across the tubes is
A U-tube filled with liquid is being rotated about an axis with angular speed ω as shown in the figure. The difference in heights of liquid in two arms is
The flow of blood in a large artery of a anesthetized dog is diverted through a ventruimeter. The wider part of the meter has a cross-sectional area equal to that of the artery, i.e., 10 mm 2 . The narrower part has an area 5 mm 2 . The pressure drop in the artery is 22 pa. Density of the blood is 1 . 06 × 10 3 kg m – 3 . The speed of the blood in the artery is
A plane is in level fight at constant speed and each of its two wings has an area of 25 m 2 . If the speed of the air on the upper and lower surfaces of the wing are 270 kmph and 234 kmph respectively,then mass of the plane is (take the density of air is 1 kg m 3
A metallic sphere with an internal cavity weighs 40 gwt in air and 20 gwt in water. If the density of the material with cavity be 8 g per cm 3 then the volume of cavity is:
The density of ice x gcm – 3 and that of water is y gcm – 3 .What is the change in volume when m g of ice melts?
A hole is made at the bottom of a tank filled with water. If the total pressure (absolute pressure) at the bottom is 3 atmosphere, then velocity of efflux is
A cubical block of copper of side 10 cm is floating in a vessel containing mercury. Water is poured into the vessel so that the copper block just gets submerged. The height of water column is ( ρ Hg = 13 . 6 g / cc , ρ Cu = 7 . 3 g / cc , ρ water = 1 gm / cc )
A water tank placed on the floor has two small holes, punched in the vertical wall, one above the other. The holes are 3.3 cm and 4.7 cm above the floor. If the jets of water issuing out from the holes hit the floor at the same point on the floor, then the height of water in the tank is
A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m 2 . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be ( ρ a i r = 1 . 2 kg / m 3 )
Two holes are made in the side of the tank such that the jets of water flowing out of them meet at the same point on the ground. If one hole is at a height of 3 cm above the bottom, them the distance of the other hole from the top surface of water is
A ball whose density is 0 . 4 × 10 3 kg / m 3 falls into water from a height of 9 cm. To what depth does the ball sink?
What is the pressure energy of a liquid of mass m and density ρ ?
A film of liquid is formed between two thin wires A and B each of mass 10 gm and length l. Now wire A is held horizontally and wire B is suspended by the liquid film. If surface tension of the liquid is 0.8 N/m, find the length l.
There is a hole of area 1 25 cm 2 in the bottom of a cylindrical vessel containing fluid up to height h, The liquid flows out in time t. If the liquid were filled in the vessel up to height 4h,then it would flow out in time
A water tank of height H, completely filled with water is placed on a level ground. It has two holes one at a depth h from top and the other at height h form its base. The water ejecting from both holes
A cylindrical tank has a hole of 3 cm 2 in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 80 cm 3 /sec. then the maximum height up to which water can rise in the tank is
Density of ice is 0.9 and that of water is 1. What will be the decrease in volume when a mass 90 gram of ice melts?
A body of density d 1 is counterpoised by Mg of weights of density d 2 in air of density d. Then the true mass of the body is
A steel block having an internal cavity weighs 234 g in air and 197 g in water. If the density of steel is 7.8 g cm – 3 , then the volume of the cavity is
A capillary tube is attached horizontally to a constant pressure head arrangement. If the radius of the capillary tube is increased by 10%, then the rate of flow of the liquid shall change nearly by
A large number of droplets, each of radius a, coalesce, to form a bigger drop of radius b. Assume that the energy released in the process is converted into the kinetic energy of the drop. The velocity of the drop is ( σ surface tension, ρ density)
A thin metal disc of radius r floats on water surface and bends the surface downwards along the perimeter making an angle θ with vertical edge of the disc. If the disc displaces a weight of water W and surface tension of water is T, then the weight of metal disc is
A ring is cut from a platinum tube 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from the pan of a balance, so that it comes in contact with the water in a glass vessel. If an extra 3.103 gf is required to pull it away from water, the surface tension of water is
An isosceles triangular plates of base 3 m and altitude 3 m is immersed in oil vertically with its base coinciding with the free surface of the oil of relative density 0.8. Determine the total thrust.
(A), (B) and (C) show three different situations of the surface of liquid contained in a vessel that is moving towards right. These figures indicate, respectively, that the vessel is :
An iceberg is floating partially immersed in sea water. If the density of sea water is 1.03 g/cc and that of ice is 0.92 g/cc, the fraction of the total volume of iceberg above the level of sea water is:
A beaker of water kept in the left pan of a common balance is counter poised with weights in the right pan. Now a body of mass 12 g and density 3 g/cc is suspended inside the beaker from an independent support and the body is completely immersed in the water without touching the sides of the beaker. To restore equilibrium the weight to be added in the right pan will be:
A liquid X of density 3.36 g/cm 3 is poured in a U-tube, which contains Hg. Another liquid Y is poured in left arm with height 8 cm. Upper levels of X and Y are same. What is density of Y?
Two communicating vessels contain mercury. The diameter of one vessel is four times larger than the diameter of the other. A column of water of height h 0 = 70 cm is poured into he left hand vessel (the narrower one). How much will be mercury level rise in the right hand vessel? (Specific density of mercury= 13.6)
A wooden rod of a uniform cross section and of length 120 cm is hinged at the bottom of the tank which is filled with water to a height of 40 cm. In the equilibrium position, the rod makes an angle of 60 0 with the vertical. The centre of buoyancy is located on the rod at a distance (from the hinge) of
Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross-sectional area 10 -6 m 2 .The breaking stress of the wire is 7 x 10 6 Nm -2 . The block is placed in a beaker of base area 200 cm 2 and initially at t= 0, the top surfaces of water and block coincide. There is a pump at the bottom corner, which ejects 2 cm 3 of water per second. If the time at which wire breaks is p x 100 seconds, then the value of p is , (Given, g=10 ms -2 )
A rectangular boat floating in water has length 4 m and breadth 1.5 m. A person gets into the boat as a result of which the boat sinks by 2 cm. Mass of the person is :
A bowl whose bottom has round holes of diameter 1 mm is filled with water. Assuming that surface tension acts only at holes, find the maximum height (in cm) up to which water can be filled in the vessel without leakage. (Given, surface tension of water = 75 x 10 -3 Nm-l , g=10 ms -2 and density of water = 1 g/cm 3 .
A container filled with liquid up to height h is placed on a smooth horizontal surface. The container is having a small hole at the bottom. As the liquid comes out from the hole, the container moves in a backward direction with acceleration a and finally, when all the liquid is drained out, it acquires a velocity v. Neglect mass of the container. In this case
What will be the length (in cm) of mercury column in a barometer tube, when the atmospheric pressure is 75 cm of mercury and the tube is inclined at an angle of 60 0 to the vertical?
A cylinder is filled with a non-viscous liquid of density d to height ho and a hole is made at a height h 1 from the bottom of the cylinder. The velocity of the liquid coming out of the hole is:
Balloon of total mass 1000 kg floats motionless over the earth’s surface. If 100 kg of sand blast are thrown over board, the balloon starts to rise with an acceleration of:
A ball of density ρ 0 falls from rest from a point p onto the surface of a liquid of density ρ in time T. It enters the liquid, stops, moves up, and returns to P in a total time 3T. Neglect viscosity, surface tension and splashing. The ratio of ρ ρ 0 is
A hollow sphere of radius R is made of metal whose specific gravity is ρ . The sphere will float in water if thickness of wall of sphere is (thickness of wall << R)
A cylindrical, tank is filled with water to a level of 3m. A hole is opened at a height of 52.5 cm from bottom. The ratio of the area of the hole to that of cross-sectional area of the cylinder is 0.1. Find the square of the velocity with which water is coming out. (g = 10 m/sec 2 )
Streamline flow is more likely for liquids with (i) high density (ii) high viscosity (iii) low density (iv) low viscosity
Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is P at a point where flow speed is v, the pressure at another point where the flow speed is 2v, is : (take density of water as ρ )
If in a satellite orbiting the earth, a cork is immersed in a jar of water and released, it will:
Consider the following statements (A) Roofs of buildings are blown off during a strong storm. (B) Roofs of buildings becomes lighter during storm. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. (B) In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) When an ice cube, floating in a glass of water melts, the water level remains unchanged. (B) The volume of ice on melting increases. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Two glass plates having a little water in between cannot be easily separated because of:
A lead shot of 1 mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by :
A small drop of water falls from rest through a-large height h in air, the final velocity is:
Water is flowing from a reservoir through two tubes of lengths l m and 16 m respectively fixed at the bottom of reservoir. The diameters of their bores are 4 mm and 8 mm respectively. The rate of flow of water in these tubes will be in the ratio of:
The profile of advancing liquid in a tube is a:
Two capillary tubes of same radius r but of lengths l 1 and l 2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the length l of the single tube that can replace the two tubes, so that the rate of flow is same as before :
Unit of surface tension is:
An iron needle slowly placed on the surface of water floats in it because:
A layer of glycerine of thickness 1 mm is present between a large surface area and a surface area of 0.1 m 2 . With what force the small surface is to be pulled, so that it can move with a velocity of 1 m/s? (Given that coefficient of viscosity= 0.07 kg-m -1 s -1 )
Which of the following processes will be least affected by the viscosity of water?
The amount of work done in forming a soap bubble (S.T. = 30 x 10 -3 N/m) of radius 5 cm is:
Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 7 5 x 10 -4 N, force due to the weight of the liquid. If the surface tension of water is 6 x 10 -2 N/m, the inner circumference of the capillary must be:
A very narrow capillary tube records a rise of 20 cm when dipped in water. When the area of cross-section is reduced to one-fourth of the former value, water will rise to a height of:
One end of a towel dips into a bucket full of water and the other end hangs over the bucket. It is found that after some time the towel becomes wet. It happens
Consider the following statements. (A) Water flows faster than honey. (B) The coefficient of viscosity of water is less than honey. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
A very long cylindrical shaped soap bubble in air has radius R. Calculate the excess pressure inside the bubble. [Surface tension of soap solution = S]
Two water droplets merge with each other to form a larger droplet. In this process:
When a capillary is dipped in mercury the level of mercury in the tube will be:
If the angle of contact is 0°, the shape of meniscus is:
Consider the following statements. (A) It is better to wash the clothes in cold soap solution. (B) The surface tension of cold solution is more than the hot solution. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Turbulence is always dissipative. (B) High reynold number promotes turbulence. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) A bubble comes from the bottom of a lake to the top. (B) Its radius increases. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Surface tension has same units as force gradient. (B) Surface tension of a liquid is force per unit length on an imaginary line drawn on the liquid surface. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) During summer surface tension of a liquid increases. (B) Thermal velocity of molecules decreases in summer. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
With the addition of salt in a liquid, the surface tension of that liquid
Figure shows two holes in a wide tank containing a liquid column. The water streams coming out of these holes strike the ground at the same point. The height of liquid column in the tank is
Two non-mixing liquids of densities ρ and n ρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL(p < l) in the denser liquid. The density d is equal to:
Fig. Shows a U-tube of uniform cross-sectional area A accelerated with acceleration a as shown. If d is the separation between the limbs, then the difference in the levels of the liquid in the U-tube is
A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is:
A solid sphere having volume V and density ρ floats at the interface of two immiscible liquids of densities ρ 1 and ρ 2 respectively. lf ρ 1 < ρ < ρ 2 , then the ratio of volume of the parts of the sphere in upper and lower liquid is
A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is
Which of the following diagrams does not represent a streamline flow?
Water flows through a frictionless duct with a crosssection varying as shown in fig. Pressure p at points along the axis is represented by
The minimum horizontal acceleration of the container so that the pressure at the point A of the container becomes atmospheric is (The tank is of sufficient height)
A U-tube contains some water. Now oil of specific gravity ‘ ρ ’ is poured in one arm. If the length oil column is 8 cm and the difference between the free surfaces of oil and water columns is 2 cm, value of ‘ ρ ’ is
Find the elastic potential energy per unit volume of water (in x10 3 Jm -3 ) at a depth of 1 km. Given, compressibility of water = 5×10 -10 SI units and density of water = 1000 kg m -3 .
Statement I: When height of a tube is less than liquid rise in the capillary tube, the liquid does not overflow. Statement II: Product of radius of meniscus and height of liquid in capillary tube always remains constant.
Water rises to height ‘h’ in caplllary tube. If the length of capillary tube above the surface of water is made less than ‘h’, then
A spherical drop of water has radius I mm If surface tension of water is 70 × 10 – 3 N/m difference of pressures between inside and out side of the spherical drop is
A container is partially filled with a liquid of density ρ 2 . A capillary tube of radius r is vertically inserted in this liquid. Now another liquid of density ρ 1 ( ρ 1 < ρ 2 ) is slowly poured in the container to a height h as shown. There is only denser liquid in the capillary tube. The rise of denser liquid in the capillary tube is also h. Assuming zero contact angle, the surface tension of heavier liquid is
A cylinder containing water up to a height of 25 cm has a hole of cross-section 1 4 cm 2 in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?
A tank has a small hole in its side at a heighty y 1 . It is filled with a liquid (density ρ ) to a height y 2 . If the absolute pressure at the top of the fluid is P t , find the velocity with which it leaves the tank. Assume that the cross- sectional area of the tank is larger as compared to that of the hole.
Three vessels A, B and C of different shapes contain a water upto the same height as shown in the figure. P A , P B and P C be the pressures exerted by the water at the bottom of the vessels A, B and C respectively. Then
A U tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are at the same level with l0 cm of water in one arm and 12.5 cm of spirit in the other as shown in figure. The relative density of the spirit is
A container is partially filled by water. A cork ball is tied to the bottom of the vessel by a string and the ball is completely submerged in water as shown in figure. The string is now cut. Then level of water in the vessel
A block of ice is completely submerged in water in a container by a string tied to the bottom of the container. When the ice is completely melted, hydrostatic pressure at the bottom of the container
Two capillary tubes made of same material having radii r and 2r are vertically dipped in the same liquid. Then due to capillary rise
Due to capillary rise in a vertical capillary tube, mass of water in the tube is m and rise of water is h. Then heat generated during the process of capillary rise is
Excess pressure in a soap bubble is 10 N/m 2 . If radius of the soap bubble is 5 mm, the total surface energy stored in the bubble is
A cube, made of a material of density 6 gm/cm 3 and having length of each side 20 cm is sliding down an inclined surface having inclination 30 o with horizontal with a velocity of 5 m/s on a layer of grease of thickness 0.2 mm. Then coefficient of viscosity of grease is
A flat plate moves normally with a speed v 1 towards a horizontal jet of water of uniform area of cross-section. The jet discharges water at the rate of volume V per second at a speed of v 2 . The density of water is ρ . Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet of water is
A uniformly tapering vessel is filled with a liquid of density 900 kg/m 3 . The force that acts on the base of the vessel due to the liquid is ( g = 10 ms − 2 )
A body of density d 1 is counterpoised by Mg of weights of density d 2 in air of density d. Then the true mass of the body is
The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is
A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration a towards right. Pressure is (i) maximum at, and (ii) minimum at
A beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the liquid will
If two liquids of same volume but different densities ρ 1 and ρ 2 are mixed, then density of mixture is given by
A streamlined body falls through air from a height h on the surface of a liquid. If d and D(D > d) represents the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is
A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes T 1 time to decrease the height of water to H η ( η > 1 ) ; and it takes T 2 time to take out the rest of water. If T 1 = T 2 , then the value of η is
As the temperature of water increases, its viscosity
The coefficient of viscosity for hot air is
A viscous fluid is flowing through a cylindrical tube. The velocity distribution of the fluid is best represented by the diagram
An incompressible fluid flows steadily through a cylindrical pipe which has radius 2r at point A and radius r at B further along the flow direction. If the velocity at point A is v, its velocity at point B is
A manometer connected to a closed tap reads 4.5 × 10 5 pascal. When the tap is opened the reading of the manometer falls to 4 × 10 5 pascal. Then the velocity of flow of water is
Two capillary of length L and 2L and of radius R and 2R are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, X = πPR 4 / 8 ηL )
A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is ω , then the difference in the heights of the liquid at the centre of the vessel and the edge is
If temperature increases, the surface tension of a liquid
A square frame of side L is dipped in a liquid. On taking out, a membrane is formed. If the surface tension of the liquid is T, the force acting on the frame will be
A thin metal disc of radius r floats on water surface and bends the surface downwards along the perimeter making an angle θ with vertical edge of the disc. If the disc displaces a weight of water W and surface tension of water is T, then the weight of metal disc is
Small liquid drops assume spherical shape because
The dimensions of surface tension are
Oil spreads over the surface of water whereas water does not spread over the surface of the oil, due to
Surface tension of a soap solution is 1 .9 × 10 − 2 N / m . Work done in blowing a bubble of 2.0 cm diameter will be
Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is
Excess pressure of one soap bubble is four times more than the other. Then the ratio of volume of first bubble to another one is
A spherical drop of water has radius 1 mm If surface tension of water is 70 × 10 − 3 N/m. Difference of pressures between inside and out side of the spherical drop is
Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement
If capillary experiment is performed in vacuum then for a liquid there
If liquid level falls in a capillary then radius of capillary will
A capillary tube of radius R is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled, mass of water that will rise in the capillary tube will now be
Two equal drops are falling through air with a steady velocity of 5 cm/sec. If the drops coalesce, the new terminal velocity will be
The terminal velocity of a rain drop of radius r falling down in the atmosphere is
What change in surface energy will be noticed when a drop of radius ff splits up into 1000 droplets of radius r. Surface tension is T.
A soap bubble has radius r.The surface tension of the soap film is T. The energy needed to double the radius of the bubble without change of temperature is
Water rises to a height of 10 cm in a capillary tube, and mercury falls to a depth of 3 . 42 cm in the same capillary tube. If the density of mercury is 13 .6 and the angle of contact is 135 o , the ratio of surface tension for water and mercury is
An aluminium sphere is dipped into water. Which of the following statement is true? [NCERT Exemplar]
A cube with a mass m = 20 g wettable by water floats on the surface of water. Each side of the cube has length l = 3 cm. The angle of contact between water and glass is zero degree and the surface tension of the water is 7.5 × 10 – 2 N/m. The distance between the lower face of the cube and the surface of the water is
A small hole of area of cross-section 2 mm 2 is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m / s 2 the rate of flow of water through the open hole would be nearly
A ball of relative density 0.8 falls into water from a height of 2m. The depth to which the ball will sink (neglect viscus force)
Three liquids of densities ρ 1 , ρ 2 a n d ρ 3 (with ρ 1 , ρ 2 > ρ 3 ), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ 1 , θ 2 a n d θ 3 obey
A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m 2 . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be ρ air = 1 . 2 kg / m 3
Which of the following statements are correct? (1) Centre of mass of a body always coincides with the centre of gravity of the body. (2) Centre of mass of a body is the point at which the total gravitational torque on the body is zero. (3) A couple on a body produces both translational and rotational motion in a body. (4) Mechanical advantage greater than one means that small effort can be used to lift a large load.
A barometer is constructed using a liquid (density = 760 kg / m 3 ). What would be the height of the liquid column, when a mercury barometer reads 76 cm? (density of mercury = 13600 kg / m 3 )
A small drop of water falls from rest through a large height h in air, the final velocity is
The heat evolved for the rise of water when one end of the capillary tube of radius r is immersed vertically into water is (Assume surface tension = T, density of water = r)
Water is flowing through a tube of inner diameter 2mm. What should be the maximum average velocity of flow of water through the tube, for which the flow will remain laminar ? Coefficient of viscosity of water at 25 o C is 8 . 90 x 10 – 4 N – s / m 2
A small ball made of Styrofoam packing material is dropped from a height of 3.0 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g – b v. After falling through 1.0 m, the ball effectively reaches terminal speed and then takes 4.0 more seconds to reach the ground. The value of the constant b is (take g = 10 m/ s 2 )
Droplets of liquid are usually more spherical in shape than large drops of same liquid because
At a certain depth of an incompressible liquid, the absolute pressure is p. At twice this depth, the absolute pressure is p 1 . Then
An open U-tube contains mercury, When 11.2 cm of water is poured into one of arms of the tube, how high does the mercury rise in the other arm from its initial level ?
A thin spherical metallic shell of radius R is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to [Thickness of the shell remains constant]
A rectangular tank of length 1 m and breadth 0.5 m is partially filled with water. When the tank is moving horizontally with a constant acceleration of 10 3 m / s 2 parallel to its length, the angle between free surface of water and horizontal will be T a k e g = 10 m / s 2
Work W is required to form a soap bubble of soap solution of volume V. What amount of work is required to be done to form a bubble of volume 8V?
Excess pressure in a soap bubble of radius R is P. What will be the excess pressure in a drop of same soap solution of radius R 8 ?
A needle is made of a material whose density is σ . Then the maximum diameter of the needle which can float on the surface of water with its length horizontal is, (surface tension of water is T)
Water flows in a horizontal tube (see figure) The pressure of water change by 700 N m − 2 between A and B where the area of cross section are 40 c m 2 and 20 c m 2 . Respectively. Find the rate of flows of water through the tube.(density of water = 1000 k g m − 3 )
Surface energy of a drop of liquid is 16mJ. When 8 of such identical drops coalesce to form a single drop
A stone tied to a string is supported from a spring scale that reads 10 N. A pan of water rests on the platform of a weighing machine and it reads 80 N. The stone is lowered into the water and the spring scale ten reads 5 N. It follows that the weighing machine
In steady state fluid flow
Gun shots are made by pouring down molten lead through a hollow pipe from the top of a tower. The molten liquid while descending breaks into drops, which are spherical due to
Capillary rise of water in a vertical glass capillary tube of radius r is 1 m what will be the excess pressure in a buble of radius 4r formed in water in a lake ? Take density of water = 1 gm/C.C and g = 10 m / s 2 .
A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5cm and the angular speed of rotation is ω r a d s − 1 . The difference in the height, h(in cm) of liquid at the center of vessel and at the side will be:
In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to : (ignore viscosity of air)
Water flows through two identical tubes A and B.A volume V 0 of water passes through the tube A and 2V 0 through B in a given time. Which of the following may be correct? a) Flow in both the tubes are steady b) Flow in both the tubes are turbulent c) Flow is steady in A but turbulent in B d) Flow is steady in B but turbulent in A
A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross – section A 1 and A 2 , are V 1 and V 2 respectively. The difference in the levels of the liquid in the two vertical tubes is h. a) The volume of the liquid flowing through the tube in unit time is A 1 V 1 . b) c) d) The energy per unit mass of the liquid is the same in both sections of the tube.
The range of attraction between molecules is of the order of
Two needles are floating on the surface of water. A hot needle when touches water surface between the needles, then they move
Which of the following is associated with liquid only and not gases?
Water contained in a tank flows through an orifice of diameter 2 cm, under a constant pressure difference of 10cm of water column. The rate of flow of water through the orifice
A metal ball of radius 'r' and density 'd' travels with a terminal velocity 'v' in a liquid of density d/4. The terminal velocity of another ball of radius '2r' and density '3d' in the same liquid is
A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
Water is flowing continuously from a tap having an internal diameter 8 × 10 –3 m.The water velocity as it leaves the tap is 0.4 ms –1 . The diameter of the water stream at a distance 2 × 10 –1 m below the tap is close to :
Tanks A and B open at the top contain two different liquids upto certain height in them. A hole is made to the wall of each tank at a depth 'h' from the surface of the liquid. The area of the hole in A is twice that of in B. If the liquid mass flux through each hole is equal, then the ratio of the densities of the liquidsrespectively, is
Two non-mixing liquids of densites ρ and nρ(n>1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL(p<1) in the denser liquid. The density d is equal to [The cylinder is completely submerged in the liquid]
Water is falling down at the rate of 1.8 Kg per minute from a vertical tube. The radius at the bottom of the tube is 0.004 m and pressure around it is 0.76m of Hg. The diameter of the tube at a height of 0.5 m from the bottom is 0.005 m. find the pressure at that point.
A thin liquid film formed between a U- shaped wire and light slider support a weight 1.5×10 –2 N (see figure). The length of the slider is 30cm and its weight negligible. The surface tension of the liquid film is
A tank with a square base of area 10m 2 is divided by a vertical partition in the middle. The bottom of the partition has a small hinged door of area 80m 2 . The tank is full of water in one compartment, and an acid (of relative density 1.7). In the other, both to a height of 4.0m. Compute necessary force to keep the door closed.
Two capillary tubes AB and BC are joined end to end at B, AB is 16cm long and of diameter 4 mm whereas BC is 4 cm long and of diameter 2 mm. the composite tube is held horizontally with A connected to a vessel of water giving a constant head of 3 cm and C is open to the air. Calculate the pressure difference between B and C
A wooden sphere is floating in water with 60% of its volume submerged in water. Now the sphere is taken to a depth of 5 m and released. What will be the acceleration of the sphere after release? Take g = 10 m / s 2
Two soap bubbles A and B of radii r and 2r are formed at the ends of two capillary tubes. If excess pressure in A is 40 N / m 2 , what is the excess pressure in B?
Along a streamline,
The pressure energy per unit volume of a liquid is
A piece of gold weighs 10 g in air and 9 g in water. What is the volume of cavity? (Density of gold = 19.3 g cm – 3 )
A boy carries a fish in one hand and a bucket (not full) of water in the other hand. If the places the fish in the bucket the weight now carried by him(assume that water does not spill):
A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then
A small ball of density r is immersed in a liquid of density σ ( > ρ ) to a depth h and released. The height above the surface of water upto which the ball will jump is
There are two holes, each of cross-sectional area a, on the opposite side of a wide rectangular tank containing a liquid of density ρ . When the liquid flows out of the holes, the net force on the tank is [h is the vertical distance between the two holes.]
A stream-lined body falls through air from a height h on the surface of a liquid. Let d and D denote the densities of the material of the body and the liquid respectively. If D > d, then the time after which the body will be instantaneously at rest is:
A body floats with one-third of its volume outside water and 3 4 of its volume outside another liquid. The density of another liquid is:
A small hole of area of cross-section 2 mm 2 present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m / s 2 , the rate of flow of water through the open hole would be nearly
In a wind tunnel experiment the pressure on the upper and lower surfaces of the wings are 0.90 × 10 5 Pa and 0 . 91 × 10 5 Pa respectively. If the area of the wings is 40 m 2 the net lifting force on the wing is
Two substances of densities ρ 1 and ρ 2 are mixed in equal volume and the relative density of mixture is 4. When they are mixed in equal masses, the relative density of the mixture is 3. The values of ρ 1 and ρ 2 are:
The volume of the hollow portion of a sphere is 3 4 of the external volume of the sphere. If it floats in a liquid at relative density 3 2 , half of its external volume immersed, the relative density of the material of the solid is
A piece of solid weighs 120g in air, 80 g in water and 60 g in a liquid, then the relative density of the solid, and that of liquid are
A metallic block weighs 15 N in air. It weighs 12 N when immersed in water and 13 N when immersed in another liquid. What is the specific gravity of the liquid?
If a block of iron(density 5 g cm – 3 ) is size 5 cm × 5 cm × 5 cm was weighed while completely submerged in water, what would be the apparent weight?
In the table shown below, column-II shows the possible outcomes to the water level of a swimming pool when a person standing on a boat in it does any one of the actions shown in column-I Column-I Column-II i. He throws a 20 kg iron anchor from the boat into the water, which then settles at the bottom ( ρ iron > ρ water ) p. It becomes lower ii. He throws out a 20 kg log of wood from the boat. The log floats on water ( ρ wood < ρ water ) q. It becomes higher iii. He empties 20 kg of water from the boat into the pool. r. It says the same iv. He drinks some water from the pool. s. Cannot be predicted from the information given Now match the given columns and select the correct option from the codes given below. Codes
A 50 kg girl wearing heel shoes balances on a single heel. The heel is circular with a diameter 1 cm. The pressure exerted by the heel on the horizontal floor is (Take g = 10 ms – 2 )
A cylindrical vessel containing a liquid is closed by a smooth piston of mass m. If A is the cross-sectional area of the piston and P 0 is the atmospheric pressure, then the pressure of the liquid just below the piston is
The work done in breaking a drop of liquid of radius R into 64 number of identical drops is [Surface tension of liquid is T]
A rectangular container having length of 0.5 m, breadth of 0.3 m and height of 0.4 m is containing water to a depth of 30 cm. A wooden block of mass 2 kg is gently released on the surface of water and it floats in water. Then hydrostatic pressure on the bottom of the container is
A small sphere of mass 6 mg is falling through a viscous liquid of specific gravity 0.8 with constant velocity of 2 cm/s. If the specific gravity of the material of the sphere is 2.4, the viscous force acting on it is
The two femurs each of cross-sectional area l0 cm 2 support the upper part of a human body of mass 40 kg. The average pressure sustained by the femurs is (Take g : l0 ms – 2 )
The force acting on a window of area 50 cm x 50 cm of a submarine at a depth of 2000 m in an ocean, the interior of which is maintained at sea level atmospheric pressure is (Density of sea water = 10 3 kg m – 3 , g = l0 ms – 2 )
A horizontal pipe line carries water in streamline flow. At a point where the cross-sectional area is 10 cm 2 the water velocity is l ms – l and pressure is 2000 pa. The pressure of water at another point where the cross-sectional area is 5 cm 2 is
A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?
A metal ball immersed in alcohol weighs W 1 at 0″C and W 2 at 50″C. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that:
Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g / cm 3 . If the mass of the other is 48g, its density in g / cm 3 is
An isosceles triangular plates of base 3 m and altitude 3 m is immersed in oil vertically with its base coinciding with the free surface of the oil of relative density 0.8. Determine the total thrust.
Water rises is a vertical capillary tube of radius 1 mm. Surface tension of water is 0.07 N/m. A and B are two points just above and just below the free surface of water in the capillary tube. The difference in pressure at A and B is
A hemispherical bowl just floats without sinking in a liquid of density 1.2 x 10 3 kg/m 3 . If the outer diameter and the density of the bowl are 1 m and 2 × 10 4 kg / m 3 , respectively, then the inner diameter of the bowl will be
A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise, distance between the plates in m is
A ball whose density is 0.4 x 10 3 kg/m 3 falls into water from a height of 9 cm . To what depth does the ball sink?
An L-shaped tube with a small orifice is held in a water stream as shown in the figure. The upper end of the tube is 10.6 cm above the surface of water. What will be the height of the jet of water coming from the orifice? Velocity of water stream is 2.45 m/s.
A tank is filled with water up to a height H. Water is allowed to come out of a hole P in one of the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D
A streamlined body falls through air from a height h on the surface of a liquid. If d and D(D > d) represents the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is
A wooden block, with a coin placed on its top, floats in water as shown in the figure. the distance I and h are shown there. After some time, the coin falls into the water. Then
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density ρ . The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is
A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both the holes are the same. Then R is equal to
A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section ,A 1 and A 2 , & velocities v 1 and v 2 respectively. The difference in the levels of the liquid in the two vertical tubes is h. Following observations are taken (i) The volume of the liquid flowing through the tube in unit time A 1 v 1 (ii) v 2 − v 1 = 2 g h (iii) v 2 2 − v 1 2 = 2 g h (iv) The energy per unit mass of the liquid is the same in both sections of the tube The correct observations is/are
A uniform rod of density ρ is placed in a wide tank containing a liquid of density ρ 0 ρ 0 > ρ . The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position the rod makes an angle θ with the horizontal
A soap bubble of radius R is blown. After heating the solution a second bubble of radius 2R is blown. The work required to blow the second bubble in comparison to that required for the first bubble is
A tube 1 cm 2 in cross section is attached to the top of a vessel 1 cm high and of cross section 100 cm 2 . Water is poured into the system filling it to a depth of 100 cm above the bottom of the vessel as shown in the figure. Take g=10 ms -2 . Find the correct statement.
The maximum force, in addition to the weight required to pull a wire of 5.0 cm long from the surface of water at temperature 20 o C is 728 dynes. The surface tension of water is
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and ρ – density of water) by
Two parallel glass plates are dipped partly in the liquid of density ‘d’ keeping them vertical. If the distance between the plates is ‘x’, surface tension for liquids is T and angle of contact is θ then rise of liquid between the plates due to capillary will be
We have two different liquids ,A and B whose relative densities are 0.75 and 1.0, respectively. If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
A block of silver of mass 4 kg hanging from a string is immersed in a liquid of relative density 0.72.If relative density of silver is 10, then tension in the string will be
A tank is filled with water of density 10 3 kg/m 3 and oil of density 0.9 x 10 3 kg/m 3 . The height of water layer is 1 m and that of the oil layer is 4 m. The velocity of efflux from an opening in the bottom of the tank is
An iceberg is floating partially immersed in sea water. The density of sea water is 1.03 g cm -3 and that of ice is 0.929 cm -3 . The approximate percentage of total volume of iceberg above the level of sea water is
An ornament weighing 36 g in air weighs only 34 g in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is 19.3 and that of copper is 8.9.
A tank is filled up to a height 2H with a liquid and is placed on a platform of height H from the ground. The height x from the ground where a small hole is punched to get the maximum range R is
The opening near the bottom of the vessel shown in the figure has an area A. A disc is held against the opening to keep the liquid from running out. Let F 1 be the net force on the disc applied by liquid and air in this case. Now the disc is moved away from the opening by a short distance. The liquid comes out and strikes the disc inelastically. Let F 2 be the force exerted by the liquid in this condition. Then F 1 /F 2 is
A water tank of height 10 m, completely filled with water is placed on a level ground. It has two holes one at 3 m and the other at 7 m form its base. The water ejecting from
A cylindrical vessel of 90 cm height is kept filled up to the brim. It has four holes 1,2,3 and 4 which are respectively at heights of 20 cm, 30 cm, 45 cm and 50 cm from the horizontal floor PQ. The water falling at the maximum horizontal distance from the vessel comes from
Figure shows a capillary tube C dipped in a liquid that wets it. The liquid rises to a point A. If we blow air through the horizontal tube H, what will happen to the liquid column in the capillary tube?
A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be
The speed of flow past the lower surface of a wing of an aeroplane is 50 ms -1 . What speed of flow over the upper surface will give a dynamic lift of 1000 Pa? Density of air = 1.3 kg m -3
A spherical liquid drop of radius R is divided into eight equal droplets. If the surface tension is 7, then the work done in this process will be
A straw 6 cm long floats on water. The water film on one side has surface tension of 50 dyne/cm. On the other side, camphor reduces the surface tension to 40 dyne/cm. The resultant force acting on the straw is
The angle of contact between glass and water is 0 o and water (surface tension 70 dyne/cm) rises in a glass capillary up to 6 cm. Another liquid of surface tension 140 dyne/cm, angle of contact 60 0 and relative density 2 will rise in the same capillary up to
A loop of 6.28 cm long thread is put gently on a soap film in a wire loop. The film is pricked with a needle inside the soap film enclosed by the thread. If the surface tension of soap solution is 0.030 N/m, then the tension in the thread is
A small metal ball of diameter 4 mm and density 10.5 g/cm 3 in dropped in glycerin of density 1.5 g/cm 3 . The ball attains a terminal velocity of 8 cm s -1 . The coefficient of viscosity of glycerin is
The velocity of small ball of mass M and density d 1 , when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is d 2 , the viscous force acting on ball is
Three identical vessels A, B and C contain same quantity of liquid. In each vessel balls of different densities but same masses are placed. In vessel A, the ball is partly submerged; in vessel B, the ball is completely submerged but floating and in vessel C, the ball has sunk to the base. If F A , F B and F C arc the total forces acting on the base of vessels A, B and C, respectively, then
When a large bubble rises from the bottom of a lake to the surface, its radius doubles. The atmospheric pressure is equal to that of a column of water of height H. The depth of the lake is:
A tank 5 m high is half filled with water and then is filled to the top with oil of density 0.85 g/cm 3 .The pressure at the bottom of the tank, due to these liquids, is:
A container containing water has a constant acceleration ‘a’ in the horizontal direction. Free surface of water gets sloped with the horizontal at angle:
Two immiscible liquids P and Q of different densities are contained in a wide U-tube as shown in Fig. 12.54. The heights of the two liquids above the horizontal line XX’ which cuts the boundary between the liquids are Hp and HQ respectively. The U-tube is transported to a planet where the acceleration of free fall is 2 3 that on the earth, where the 3 liquids do not evaporate and where the heights of liquid (measured relative to XX’ ) are h p and h Q respectively. Which of the given statements is correct?
An inverted (bell) lying at the bottom of a lake 47.6 m deep has 50 cm 3 of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be atmospheric pressure = 70 cm of Hg and density of Hg= 13.6 g/cm 3 ):
A given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in Fig. 12.52. If the tube is rotated with a constant angular velocity ω then :
A vessel contains liquid of density σ filled to a height H. The vessel is placed at rest. Average pressure exerted by the liquid on the wall is:
If the system is not in free fall, which of the following statements are true about hydrostatic pressure? (i) In a liquid points at different depths can never be at same pressure. (ii) In a liquid points at different depths may be at same pressure. (iii) In different liquids points at same depth can never be at same pressure. (iv) In different liquids points at same depth can be at same pressure. (v) In different liquids points at different depths can be at same pressure.
A square gate of size 2m x 2m is hinged at its mid-point. A fluid of density σ fills the space to the left of the gate. The force F required to hold the gate stationary is:
When a body is weighed in a liquid, the loss in its weight depends upon:
A dam for water reservoir is built thicker at the bottom than at the top because:
Which of the following would a hydrogen balloon find easier to lift?
A U-tube is partially filled with water. Oil, which does not mix with water, is next poured into one side until water rises by 25 cm on the other side. If the density of oil be 0.8, the oil level will stand higher than the water level by:
A person is carrying a bucket of water in one hand and a block in the other hand. After putting the block in the bucket in which the block floats, the person carries :
The spring balance A reads 2 kg with a block suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in Fig. 12.64. In this situation: (i) the balance A will read more than 2 kg (ii) the balance B will read more than 5 kg (iii) the balance A will read less than 2 kg and B will read more than 5 kg (iv) the balances A and B will read 2 kg and 5 kg respectively
A streamlined body falls through air from a height h on the surface of a liquid. If d and D (> d) represent the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is:
A fisherman hooks an old log of wood of weight 12 N and volume I000 cm 3 . He pulls the log half way out of water. The tension in the string at this instant-is:-
A body weighs 40 g in air. If its volume is 10 cc, in water it will weigh:
For a body floating in water the apparent weight is equal to:
A vessel contains oil (density 0.8 g/cc) over mercury (density 13.6 g/cc). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in g/cc is:
A beaker containing water is counter poised on a balance. If a finger is immersed in water so that it does not touch the bottom or the side of the beaker, the pan on which the beaker rests will:
A boat 3 m long and 2 m wide is floating in a lake. When a man climbs over it, it sinks 1 cm further into water. The mass of the man is:
If a sample of metal weighs 210 g in air, 180 g in water and 120 g in a liquid: (i) RD of metal is 3 (ii) RD of metal is 7 (iii) RD of liquid is 3 (iv) RD of liquid is ( 1/3)
A beaker containing water weighs 100 g. It is placed on the pan of a balance and a piece of metal weighing 70 g and having a volume of 10 cm 3 is placed inside water in the beaker. The weight of the beaker and the metal would be:
When a body of density ρ and volume V is floating in a liquid of density σ : (i) its true weight is Vρg (ii) loss in its weight is Vσg (iii) its apparent weight is zero (iv) its density ρ is lesser than that of liquid σ
When a piece of ice floating in a beaker of water completely melts, the level of water in the beaker:
An ice cube containing a lead piece in it is floating in a glass of water. As ice melts the water level will:
How high (in m) would water rise in the pipes of a building, if the water pressure gauge shows the pressure at the ground floor to be 270 kPa.
A man is sitting in a boat which is floating in a pond. If the man drinks some water from the pond, the level of water in the pond will:
The tension in a string holding a solid block below the surface of a liquid (where ρ liquid > ρ block ) as in shown in the figure is T 0 when the system is at rest. Then what will be the tension in the string if the system has upward acceleration a?
Neglecting the density of air, the terminal velocity obtained by a raindrop of radius 0.3 mm falling through the air of viscosity 1.8 x 10 -5 N/m 2 will be
Water (density ρ ) is flowing through the uniform tube of cross-sectional area A with a constant speed v as shown in the figure. The magnitude of force exerted by the water on the curved corner of the tube is (neglect viscous forces)
One end of a long iron chain of linear mass density /, is fixed to a sphere of mass m and specific density 1/3 while the other end is free. The sphere along with the chain is immersed in a deep lake. If specific density of iron is 7, the height h above the bed of the lake at which the sphere will float in equilibrium is (Assume that the part of the chain lying on the bottom of the lake exerts negligible force on the upper part of the chain):
A horizontal oriented tube AB of length 5 m rotates with a constant angular velocity 0.5 rad/s about a stationary vertical axis OO’ passing through the end A. The tube is filled with ideal fluid. The end of the tube is open, the closed end B has a very small orifice. The velocity with which the liquid comes out from the hole (in m/s) is
A sphere of solid material of density d has a concentric spherical cavity of radius r. lf it just floats in water, i-e-, with its upper surface touching the water surface, then R and r ate related as: (Take density of water = 1)
A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body?
A cylinder fitted with piston as shown in figure. The cylinder is filled with water and is taken to a place where there is no gravity. Mass of the piston is 50 kg. The system is accelerated with acceleration 0.5 m/ sec 2 in positive x-direction. Find the force exerted by fluid on the surface AB of the cylinder in decanewton. Take area of cross-section of cylinder to be 0.01 m 2 and neglect atmospheric pressure (1 decanewton =10 N).
A wooden block, with a coin placed on its top, floats in water as shown in the figure. The distance h and/ are shown there. After sometime, the coin falls into the water. Then:
A body of mass 120 kg and density 600 kg/m 3 floats in water. What additional mass could be added to the body so that the body will just sink?
Two spheres each of volume 250 cc but of relative densities 0.8 and 1.2 are connected by a string and the combination is immersed in a liquid in vertical position as shown in the figure. The tension in the string k 18 N. The value of k is . (Given, g=10 ms -2 )
A glass flask having mass 390 g and an interior volume of 500 cm 3 floats on water, when it is less than half filled with water. The density of the material of the flask is:
A siphon has a uniform circular base of diameter 8 π cm with its crests 1.8 m above water level as in figure. The absolute pressure at the crest level A(in kPa) is . U s e P 0 = 10 5 N / m 2 and g = 10 m / s 2
Action of a paint-gun is based on:
A cylindrical vessel of height hand base area S is filled with water. An orifice of area s < < S is opened in the bottom of the vessel. Neglecting the viscosity of water determine how soon all the water will flow out of the vessel?
Fig. represents vertical sections of four wings moving horizontally in air. In which case is the force upwards?
A uniform rod of length b = 90 cm capable of turning about its end which is out of water, rests inclined to the vertical. If its specific gravity is 5/9,the length immersed in water (in cm) is
A vessel open at top contains 50 litres of water. A small opening is made at the bottom of vessel. It is observed that 3 litres of water comes out in time t 1 , the next 3 litres in a further time t 2 and the next 3 litres in further time t 3 , then:
A tube with both ends open floats vertically in water. Oil with a density 800 kg/m 3 is poured into the tube. The tube is filled with oil up to the top end while in equilibrium. The portion out of the water is of length 10 cm. The length of the tube is:
Liquid is filled to a height ‘h’ in a vessel whose side walls are vertical. A hole is made in one of the side walls at depth h’ below the surface of liquid such that water emerging from hole strikes the ground at maximum horizontal distance, then:
The pressures of water in a water pipe when the tap is closed and open are respectively 3.5 x 10 5 N/m 2 and 3 x 10 5 N/m 2 . The velocity of water flowing through the pipe when the tap is open is:
An L-shaped glass tube is just immersed in flowing water such that its opening is pointing against flowing water. If the speed of water current is v, then:
A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then R, is equal to:
A water tank resting on the floor has two small holes vertically one above the other. The holes are h 1 cm and h 2 cm above the floor. How high does water stand in the tank if the jets from the holes hit the floor at the same point?
Water is poured in a tank through a cylindrical tube of area of cross-section A and ejecting water at a constant speed 4 m/s. The tank contains a hole of area A/2 at bottom. Level of water in the tank will not go up beyond: (take g = 10 m/s 2 )
A small ball of density ρ is immersed in a liquid of density σ ( > ρ ) to a depth h and released. The height above the surface of water up to which the ball will jump is
A ball floats on the surface of water in a container exposed to atmosphere. If the container is covered and air is compressed, the ball will:
A boat with scrap iron is floating in a lake. If the scrap iron is thrown in the lake the water level will:
A vessel contains an immiscible mixture of water and a liquid of density 0.8 gm/cc. A cube of side 10 cm is placed in the mixture and it is observed that the water-liquid interface is at the middle of cube height.Mass of the cube is:
Water flows through a frictionless duct with a cross-section varying as shown in Fig. Pressure p at points along the axis is represented by:
Water is flowing through a horizontal pipe of varying cross-section. If the pressure of water equals 2 cm of mercury, where the velocity of the flow is 35 cms -1 , what is the pressure at another point, where the velocity of flow is 65 cms -1 ?
The speeds of air-flow on the upper and lower surfaces of a wing of an aeroplane are v 1 and v 2 respectively. If A is the cross-sectional area of the wing and ‘p’ is the density of air, then the upward lift is :
Consider the following statements (A) The blood pressure in humans is greater at the feet than at the brain. (B) Pressure of liquid column is proportional to height, density of liquid and acceleration due to gravity. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) Two identical spheres, one solid and the other hollow are immersed completely in water. The solid sphere will experience greater upthurst. (B) The upthurst is directly proportional to mass of the body. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
A firehose of diameter 8 cm is connected with a metallic pipe of diameter 2 cm. If. pressure and velocity of water in firehose is 5 × 10 6 N / m 2 and 2 m/s respectively. Find the pressure in the metal pipe.
Consider the following statements (A) The velocity of flow of a liquid is smaller when pressure is larger and vice-versa. (B) According to Bernoulli’s theorem, for the stream line flow of an ideal fluid, the total energy per unit mass remains constant. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) A piece of cork embedded inside an ice block, floats in water. If ice melts completely, the water level remains unchanged. (B) Ice and water have same density. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) As wind flows left to right and a ball is spinned as shown, there will be a lift of the ball. (B) Decrease in velocity of air below the ball, increases the pressure more than that above the ball. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Liquid flows through two capillary tubes connected in series. Their lengths are L and 2L and radii r and 2r respectively. The pressure difference across the first and second tube are in the ratio :
A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to:
The pressure difference inside and outside a soap bubble is:
A water drop is divided into eight equal droplets. The pressure difference between the inner and outer side of the big drop will be:
On putting a capillary tube in a pot filled with water, the level of water rises upto a height of 4 cm in the tube. If a tube of half the diameter is used, the water will rise to the height of nearly:
A soap bubble is blown slowly at the end of a tube by a pump supplying air at a constant rate. Which one of the following graphs represents the correct variation of the excess of pressure inside the bubble with time?
Kerosene oil rises in the wick of a lantern because of:
Fig. shows a capillary tube dipped in water. If P is the atmospheric pressure, P x the pressure at x and P Y the pressure at y then :
If two soap bubbles of radii R 1 and R 2 are combined in vacuum (in isothermal conditions) to form a single soap bubble, then radius of combined soap bubble is :
Water risesin a capillary to a height H when the capillary is vertical. If the same capillary is now inclined to the vertical, the vertical height of water level in it will:
A liquid drop of radius R breaks into 64 tiny drops each of radius r. If the surface tension of liquid is T, then the gain in energy is:
Consider the following statements. (A) A large force is required to draw apart normally two glass plates enclosing a thin water film. (B) Water works as glue and sticks two glass plates Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Surface tension is the property of only liquids. (B) Only liquids have free surface in fluids. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Surface energy of an oil drop is same whether placed on glass or water surface. (B) Surface energy is dependent only on the properties of oil.
Consider the following statements. (A) At critical temperature, surface tension of a liquid becomes zero. (B) At critical temperature, intermolecular forces for liquids and gases become equal. Also liquid can expand without any restriction Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) A needle placed on the surface of the liquid may float whereas a ball of same material will always sink. (B) Upthurst (or buoyancy) does not depend on material of object. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Figure shows two holes in a wide tank containing a liquid common. The water streams coming out of these holes strike the ground at the same point. The height of liquid column in the tank is
A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side ‘L’ at a depth ‘4y’ from the top and the other is a circular hole of radius ‘R’ at a depth ‘y’ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, ‘R’ is equal to:
The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is:
A cubical block of wood l0 cm on a side floats at the interface between oil and water, as in Fig. with its lower face 2 cm below the interface. The intensity of the oil is 0.6 g cm – 3 . The mass of the block is
A mercury barometer reads 75 cm in vertical position. If the tube is inclined by 60 0 to the vertical, the length of the mercury in the tube will be
A closed rectangular vessel completely fllled with a liquid of density ρ moves with an acceleration a = g. The value of the pressure difference at point A and B i.e., ( P 1 – P 2 ) is:
An incompressible liquid travels as shown in Fig. The speed of the fluid in the lower branch will be
A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g 3 , the fraction of volume immersed in the liquid will be
The vertical sections of the wing of a fan are shown. Maximum upthrust is in
To get the maximum flight a ball must be thrown as:
The acceleration a of the vertical U-tube is
Water flows at 10 c.c./s through an opening at the bottom of a tank in which the water is 2m deep. The rate of flow of water if an additional pressure of 20kpa is applied to the top of water will be
Water having density ‘⍴’ is flowing (steadily) downwards in the given tube. What is the relation between P A & P B ?
If the terminal speed of a sphere of gold (density: 19.5 kg / m 3 ) is 0.2 m/s in viscous liquid (density : 1.5 kg / m 3 ), find the terminal speed of a sphere of silver (density : 10.5 kg / m 3 ) of the same size in the same liquid.
A vessel, whose bottom has round hole with diameter 0.1 mm, is filled with water. The maximum height upto which water can be filled without leakage is (Surface tension of water is 75 dyne/cm)
A spherical ball of mass 4 m, density σ and radius r is attached to a pulley-mass system as shown in figure. The ball is released in a liquid of coefficient of viscosity η and density ρ ( < σ 2 ) If the length of the liquid column is sufficiently long, the terminal velocity attained by the ball is given by (assume all pulleys to be massless and string as massless and inextensible):
If the radius of a soap bubble is four times that of another, then the ratio of their pressures will be
If work done in increasing the size of a soap film from 10 cm x 6 cm to 10 cm x 11 cm is 2 x 10 – 4 J, then the surface tension is
A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
Three liquids of densities ρ 1 , ρ 2 and ρ 3 ( with ρ 1 > ρ 2 > ρ 3 ) having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ 1 , θ 2 and θ 3 obey
Calculate the pressure inside a small air bubble of radius r situated at a depth of h below the free surface of liquids of densities ρ 1 and ρ 2 and surface tensions T 1 and T 2 . The thickness of first and second liquids are h 1 and h 2 . Take atmosphere pressure = P 0 .
A block of ice of area A and thickness 0.5 m is floating in the fresh water. In order to just support a man of 100 kg, find the area A. (the specific gravity of ice is 0.917 and density of water = 1000 kg/ m 3 ).
A homogeneous solid cylinder of length L (L < H 2 ). Crosssectional area A 5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L 4 in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure P 0 . Then density D of solid is given by
Find the force acting on the piston of 3 cm 2 at point 2 due to the water column of height 10 m.
A container shown in figure contains a liquid to a depth H, and of density ρ . The gauge pressure at point P is:
A smooth gate is kept in equilibrium by applying a horizontal force. What is the value of y so that no horizontal reaction force acts at the Pivot?
A U-tube in which the cross-sectional area of the limb on the left is one quarter, the limb on the right contains mercury (density 13.6 g/ cm 3 ). The level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?
An open pan P filled with water p (density ρ w ) is placed on a vertical rod, maintaining equilibrium. A block of density ρ is placed on one side of the pan as shown. Water depth is more than height of the block.
A metallic cube of mass ‘m’ is suspended by a string. Area of each face is ‘A’. If p be the hydrostatic pressure on the bottom face of the cube, then
When an aircraft is flying, let V 1 be the speed of air just below the wings and V 2 be the speed of air just above the wing. Then
A container of large cross-sectional area has a small orifice at its bottom. The container is filled with water upto a height of ‘h’ above the orifice and mass flow rate of water through the orifice is 2 Kg/sec. If the height of water surface above the orifice is made 4h and cross-sectional area of the orifice is doubled, then mass flow rate of water will be
Three immiscible and non-reacting liquids of densities P, 2P and P/2 are in a U-tube as shown in the figure. Free surfaces of liquids in the two arms of the U-tube are in the same horizontal level. Then the length ‘x’ of the liquid column of density P 2 is [l = 27 cm]
When a viscous liquid is flowing through a horizontal capillary tube. The flow is laminar, difference in pressure between the ends of the pipe is Δ p and the discharge is found to be Q. When two such identical tubes are connected in series , what should be the difference in pressure between its ends if the discharge through it is 2Q?
Figure shows four containers of olive oil. The pressure at depth h is
A body floats in a liquid contained in a beaker. If the whole system as shown in figure falls freely under gravity, then the upthrust on the body due to liquid is
The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 10 4 . The height of the hill is
Density of ice is ρ and that of water is σ . What will be the decrease in volume when a mass M of ice melts
A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be
When a large bubble rises from the bottom of a lake to the surface. Its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is
The value of g at a place decreases by 2%. The barometric height of mercury
Three liquids of densities d,2d and 3d are mixed in equal volumes. Then the density of the mixture is
A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 kgm –3 . The velocity with which gasoline begins to shoot out of the hole is
An L-shaped tube with a small orifice is held in a water stream as shown in fig. The upper end of the tube is 10.6 cm above the surface of water. What will be the height of the jet of water coming from the orifice? Velocity of water stream is 2.45 m/s
Fig. represents vertical sections of four wings moving horizontally in air. In which case the force is upwards
An L-shaped glass tube is just immersed in flowing water such that its opening is pointing against flowing water. If the speed of water current is v, then
Velocity of water in a river is
A small drop of water falls from rest through a large height h in air; the final velocity is
Two capillaries of same length and radii in the ratio 1 : 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is 1 m of water, the pressure difference across first capillary is
When a body falls in air, the resistance of air depends to a great extent on the shape of the body, 3 different shapes are given. Identify the combination of air resistances which truly represents the physical situation. (The cross sectional areas are the same).
Water falls from a tap, down the streamline
A U-tube in which the cross-sectional area of the limb on the left is one quarter, the limb on the right contains mercury (density 13.6 g/cm 3 ). The level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water
A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then
A vessel contains oil (density = 0.8 gm/cm 3 ) over mercury (density = 13.6 gm/cm 3 ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm 3 is
From amongst the following curves, which one shows the variation of the velocity v with time t for a small sized spherical body falling vertically in a long column of a viscous liquid
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel (s = relative density of mercury and ρ = density of water) by
The value of surface tension of a liquid at critical temperature is
When there is no external force, the shape of a liquid drop is determined by
Surface tension is due to
A pin or a needle floats on the surface of water, the reason for this is
The spiders and insects move and run about on the surface of water without sinking because
A drop of oil is placed on the surface of water. Which of the following statement is correct
On mixing the salt in water, the surface tension of water will
The maximum force, in addition to the weight required to pull a wire of 5.0 cm long from the surface of water at temperature 20 o C, is 728 dynes. The surface tension of water is
Mercury does not wet glass, wood or iron because
If a glass rod is dipped in mercury and withdrawn out, the mercury does not wet the rod because
The force required to separate two glass plates of area 10 − 2 m 2 with a film of water 0.05 mm thick between them, is (Surface tension of water is 70 × 10 − 3 N/m)
The force required to take away a flat circular plate of radius 2 cm from the surface of water, will be (the surface tension of water is 70 dyne/cm)
Two droplets merge with each other and forms a large droplet. In this process
Radius of a soap bubble is ‘r’, surface tension of soap solution is T. Then without increasing the temperature, how much energy will be needed to double its radius
The surface tension of a liquid is 5 N/m. If a thin film of the area 0.02 m2 is formed on a loop, then its surface energy will be
The surface tension of a liquid at its boiling point
The work done in blowing a soap bubble of 10 cm radius is (Surface tension of the soap solution is 3 100 N / m )
The work done in increasing the size of a soap film from 10 cm× 6 cm to 10 cm × 11 cm is 3 ×10 -4 joule. The surface tension of the film is
A liquid drop of diameter D breaks upto into 27 small drops of equal size. If the surface tension of the liquid is σ , then change in surface energy is
One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is
Which of the following statements are true in case when two water drops coalesce and make a bigger drop
If σ be the surface tension, the work done in breaking a big drop of radius R into n drops of equal radius is
8000 identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is
The surface energy of liquid film on a ring of area 0.15 m 2 is (Surface tension of liquid = 5 N m − 1 )
A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. (Surface tension of mercury is 0 .465 J / m 2 )
A liquid does not wet the sides of a solid, if the angle of contact is
A liquid film is formed in a loop of area 0.05 m 2 . Increase in its potential energy will be (T = 0.2 N/m)
The meniscus of mercury in the capillary tube is
What is the shape when a non-wetting liquid is placed in a capillary tube
A soap bubble assumes a spherical surface. Which of the following statement is wrong
A long cylindrical glass vessel has a small hole of radius ‘r’ at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension T) without any water entering inside is
If the surface tension of a soap solution is 0.03 MKS units, then the excess of pressure inside a soap bubble of diameter 6 mm over the atmospheric pressure will be
The radii of two soap bubbles are r 1 and r 2 . In isothermal conditions, two meet together in vacuum. Then the radius of the resultant bubble is given by
The adjoining diagram shows three soap bubbles A, B and C prepared by blowing the capillary tube fitted with stop cocks, S 1 , S 2 and S 3 . With stop cock S closed and stop cocks S 1 , S 2 and S 3 opened
There are two liquid drops of different radii. The excess pressure inside over the outside is
If the radius of a soap bubble is four times that of another, then the ratio of their pressures will be
Two bubbles A and B (A > B) are joined through a narrow tube. Then
Two capillary tubes P and Q are dipped in water. The height of water level in capillary P is 2/3 to the height in Q capillary. The ratio of their diameters is
A vessel, whose bottom has round holes with diameter of 0.1mm, is filled with water. The maximum height to which the water can be filled without leakage is (S.T. of water =75 dyne/cm, g =1000 cm/s 2 )
It is not possible to write directly on blotting paper or newspaper with ink pen
Two capillary tubes of radii 0.2 cm and 0.4 cm are dipped in the same liquid. The ratio of heights through which liquid will rise in the tubes is
The action of a nib split at the top is explained by
Water rises upto a height h in a capillary on the surface of earth in stationary condition. Value of h increases if this tube is taken
Water rises in a vertical capillary tube upto a height of 2.0 cm . If the tube is inclined at an angle of 60 o with the vertical, then upto what length the water will rise in the tube
A shell having a hole of radius r is dipped in water. It holds the water upto a depth of h then the value of r is
In a capillary tube, water rises by 1.2 mm. The height of water that will rise in another capillary tube having half the radius of the first, is
Radius of a capillary is 2 × 10 − 3 m . A liquid of weight 6 .28 × 10 − 4 N may remain in the capillary then the surface tension of liquid will be
If water rises in a capillary tube upto 3 cm. What is the diameter of capillary tube (Surface tension of water = 7.2 ×10 –2 N/m)
When a capillary is dipped in water, water rises 0.015 m in it. If the surface tension of water is 75×10 –3 N/m, the radius of capillary is
The surface tension for pure water in a capillary tube experiment is
Water rises up to a height h in a capillary tube of certain diameter. This capillary tube is replaced by a similar tube of half the diameter. Now the water will rise to the height of
Kerosene oil rises up the wick in a lantern
A steel ball of radius 2 mm of relative density 8 .2 is falling through a liquid of relative density 1.9. Its terminal velocity is 0.7 m/s. What is the viscosity of the liquid if acceleration due to gravity is 10 m/s 2 ?
A sphere of radius R and density ρ 1 is dropped in a liquid of density σ . Its terminal velocity is v 1. If another sphere of radius R and density ρ 2 is dropped in the same liquid, its terminal velocity will be
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary will be :
Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 75 x 10- a N force due to the weight of the liquid. If the surface tension of water is 6 ^ × 10 − 2 Nm − 1 , the inner circumference of the capillary must be
The surface tension of soap solution is 25 × 10 − 3 Nm − 1 The excess of pressure inside a soap bubble of diameter 1 cm is
A number of water droplets each of radius coalesce to form a droplet of radius fl. The rise in temperature d θ is
If T is surface tension of soap solution, the amount of work done in blowing a soap bubble from diameter D to a diameter 2 D is
Energy needed in breaking a drop of radius R into n drops of radius r, is
The work done in splitting a drop of water of 1 mm radius into 10 6 droplets is [S.T. of water 72 × 10 − 3 J / m 2
Find the difference of air pressure between the inside and outside a soap bubble 5 mm in diameter, if the surface tension is 1.6 N – 1
To what height h should a cylindrical vessel of diameter d be filled with a liquid so that the total force on the vertical surface of the vessel be equal to the force on the bottom ?
A hemispherical portion of radius -R is removed from the bottom of a cylinder of radius R. The volume of remaining cylinder is V and its mass is M. It is suspended by a string in a liquid of density ρ , where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is
A non viscous liquid of constant density 500 kg/m3 flows in a variable cross-sectional tube [Fig. (6)]. The area of cross section of the tube at the two points P and Q at heights of 3 m and 6 m are 2×10 -3 m 3 and 4×10 -3 m 3 respectively. The work done per unit volume by the forces of gravity as fluid flows from point P to Q is
Water rises to a capillary tube to a height of e cm. If the area of cross section of the tube is one-fourth, the water will rise to a height of
The radius of the bore of a capillary tube is r and the angle of contact of the liquid is θ . When the tube is dipped in the liquid, the radius of curvature of the meniscus of liquid rising in the tube is
Liquid drops are falling slowly one by one from a vertical glass tube. Establish a relation between the weight of a drop w, the surface tension land the radius r of the tube (assume the angle of contact to be zero)
A drop of water of volume V is pressed between the two glass plates so as to spread to an area A. If T be the surface tension, the normal force required to separate the glass plates is
If a section of soap bubble (of radius r) through its center is considered, the force on one half due to surface tension is
If water has a surface tension of 7 × 10 − 2 N / m 2 and an angle of contact with glass is zero, it rises in a capillary of diameter 0. 5mm to a height
The ratio of excess of pressure in two soap bubbles is 3 : 1. The ratio of their volumes will be
Drops of liquid of density d are floating half immersed in a liquid of density p. If the surface tension of liquid is T, then radius of the drop will be
A soap bubble formed at the end of the tube is blown very slowly. The graph between excess of pressure inside the bubble with time is
A rod of length 6 m has specific gravity ρ ( = 25 / 36 ) . One end of the rod is tied to a 5 m long rope, which in turn is tied to the floor of a pool 10 m deep, as shown. Find the length (in m) of the part of rod which is out of water.
An open tank 10 m long and 2 m deep is filled up to 1.5 m height of oil of specific gravity 0.82. The tank is uniformly accelerated along its length from rest to a speed of 20 m/s horizontally. The shortest time in which the speed may be attained without spilling any oil is
A vessel contains oil (density = 0.8 g/cm 3 ) over mercury (density 13.6 g/cm 3 ). A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of sphere in g/cm 3 is
A loop of 6.28 cm long thread is put gently on a soap film in a wire loop. The film is pricked with a needle inside the soap film enclosed by the thread. If the surface tension of soap solution is 0.030 N/m, then the tension in the thread is
A glass tube 80 cm long and open at both ends is half immersed in mercury. Then the top of the tube is closed and it is taken out of the mercury. A column of mercury 20 cm long then remains in the tube. The atmospheric pressure (in cm of Hg) is
Two cylinders of same cross section area and length L but made of two material of densities d 1 and d 2 are connected together to form a cylinder of length 2L. The combination floats in a liquid of density d with a length L/2 above the surface of the liquid. If d 1 > d 2 then
The radius of the bore of a capillary tube is r and the angle of contact of the liquid is θ . When the tube is dipped in the liquid, the radius of curvature of the meniscus of liquid rising in the tube is
A liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis. The liquid rises at its sides. The radius of the vessel is 0.05 m and the speed of rotation is 2 revolutions per second. The difference in the heights of the liquid at the centre and at the sides of the vessel will be (take g = 10 ms – 2 and π 2 = 10 )
A small sphere of radius‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
A soap bubble of initial radius r is to be blown up. The surface tension of the soap film is T. The surface energy needed to double the diameter of the bubble without change in temperature, is
When a ball is released from rest inside a very long viscous liquid, its downward acceleration is ‘a’ (just after release). Find the acceleration of the ball when the ball has acquired two third of its maximum velocity.
A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then
A capillary tube of radius r is lowered into a liquid of surface tension T and density ρ . Given angle of contact = 0 o . The work done by surface tension will be
The tension in a string holding a solid block below the surface of a liquid (where d liquid > d block ) as in shown in the figure is T when the system is at rest. Then what will be the tension in the string if the system has upward acceleration a?
Two non-mixing liquids of densities ρ and n ρ ( n > 1 ) are put in a container. The height of each liquid is h . A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length p L ( ? < 1 ) in the denser liquid. The density d is equal to
In a capillary tube of glass having radius 0.5 mm, the height upto which water can be filled without any dripping out (surface tension of water is 0.15 SI units)
A small iron ball falls through a viscous liquid at a constant speed of 20cm/sec. If the steel ball is pulled upwards with a force equal to twice its effective weight, how will it move upward?
A raindrop reaching the ground with terminal velocity has momentum p. Another drop of twice the radius also reaching the ground with terminal velocity, will have momentum
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2 . 5 × 10 – 2 N / m . The pressure inside the bubble equals at a point Z 0 below the free surface of water in a container. Taking g = 10 m / s 2 density of water 10 3 kg / m 3 , the value of Z 0 is
The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is
Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then
The wettability of a surface by a liquid depends primarily on
A gas bubble of diameter D rises steadily through a solution of density ρ at the rate of v. The coefficient of viscosity of the solution is
One thousand small water drops of equal radii combine to form a bigger drop. The ratio of final surface energy to the total initial surface energy is
A rectangular film of liquid is extended from 4 c m × 2 c m to 5 c m × 4 c m . If the work done is 3 × 10 – 4 J the value of the surface tension of the liquid is
Two metal spheres are falling through a liquid of density 2 × 10 3 k g / m 3 with the same terminal speed. The material density of sphere 1 and sphere 2 are 8 × 10 3 k g / m 3 a n d 11 × 10 3 k g / m 3 respectively. The ratio of their radii is:
When water flows at a rate Q through a tube of radius r placed horizontally, a pressure difference p develops across the ends of the tube. If the radius of the tube is doubled and the rate of flow halved, the pressure difference will be:
The approximate depth of an ocean is 2700 m. The compressibility of water is 45 . 4 × 10 – 11 Pa – 1 and density of water is 10 3 kg / m 3 . What fractional compression of water will be obtained at the bottom of the ocean?
A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?
A light cylindrical vessel is kept on a horizontal surface. It’s base area is A. A hole of cross sectional area a is made just at its bottom side. The minimum coefficient of friction necessary to stop sliding of the vessel due to impact force of the emerging liquid is (a << A).
A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is
A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:
A liquid does not wet the solid surface if angle of contact is
When a ball is released from rest in a very long column of viscous liquid, its downward acceleration is “a” (just after the release). Then its acceleration when it has acquired 3/5 of maximum velocity is x a y , find x + y.
A boy carries a fish in one hand and a bucket ( not full ) of water in the other hand. If he places the fish in the bucket , the weight now carried by him ( assume that water doesn’t spill )
A hollow sphere of radius R is made of a metal whose specific gravity is ρ . The sphere will float in water if the thickness of wall of the sphere is (density of water is 1 gm/cc)
An isosceles triangular plate of base 3m and altitude 3m is immersed in oil vertically with its base coinciding with the free surface of the oil of relative density 0.8. Determine the total thrust.
Along a streamline
In a u-tube as shown in the fig. water and oil are in the left side and right side of the tube respectively. The heights from the bottom for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is [ take ρ water = 1000 kg / m 3
A deep rectangular pond of surface area A, containing water (density = ρ ), specific heat capacity = s), is located in a region where the outside air temperature is at a steady value of –26°C. The thickness of the frozen ice layer in this pond, at a certain instant is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of ice layer, at this instant, would be given by
Two small spherical metal balls, having equal masses, are made from materials of densities ρ 1 and ρ 2 ( ρ 1 = 8 ρ 2 ) and have radii of 1 mm and 2 mm, respectively, they are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0 . 1 ρ 2 . The ratio of their terminal velocities would be,
Regarding liquid the wrong statement among the following is
A ball of relative density 0.8 falls into water from a height of 2 m. The depth to which the ball will sink is
A cylindrical container of cross sectional area 1 m 2 is partially filled by water to a depth of 50 cm. Now a cube of size 10 c m × 10 c m × 10 c m , and specific gravity 0.8 is gently placed on the free surface of water. Then increase in pressure at the bottom of container is
A U–tube contains some non–viscous liquid upto a depth h. The tube starts moving to the right parallel to its base with constant acceleration ‘a’. Find the height of liquid column in arm(1)
Terminal velocity of a steel sphere of radius r in a viscous liquid of density ρ and coefficient of viscosity η is v. What will be the terminal velocity of a steel sphere of radius 2r in another viscous liquid of density ρ and coefficient of viscosity 2 η ?
Eight identical drops of mercury each of radius ‘r’ coalesce to form a single drop. If surface tension of mercury is ‘T’, the heat generated is
Water rises in capillary up to a certain height such that the upward force of surface tension balances the force of 75 × 10 − 4 N due to weight of the liquid. If surface tension of water is 6 × 10 − 2 N / m , The internal circumference of the capillary must be
If F C and F A denote cohesive and adhesive forces on a liquid molecule near the surface of solid, Then the surface of liquid is concave, when
A tank is filled with water of density 103 kg/ m 3 and oil of density 9 x 103 kg/ m 3 . The height of water layer is 1 m and that of the oil layer is 4 m. The velocity of efflux from an opening in the bottom of the tank is
A cube is shifted to a depth of 100 m is a lake. The change in volume is 0.1%. The bulk modulus of the material is nearly
We have two different liquids A and B whose relative densities are 0.75 and 1.0, respectively. If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
A water drop is divided into eight equal droplets. The pressure difference between inner and outer sides of the big drop
A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g/3, the fraction of volume immersed in the liquid will be
The correct relation is
A spherical steel ball released at the top of a long column of glycerine of length l, falls through a distance l/2 with accelerated motion and the remaining distance l/2 with uniform velocity. Let t 1 and t 2 denote the times taken to cover the first and second half and W 1 and W 2 the work done against viscous force in the two halves, then
A solid shell loses half its weight in water Relative density of shell is 5. What fraction of its volume is hollow
Two particles are shown in figure. At time t = 0, a constant force F = 6N starts acting on the 3 kg particle. The velocity of the centre of mass of these particles at t = 5s is
An ideal fluid flows in the pipe as shown in the figure. The pressure in the fluid at the bottom P 2 is the same as it is at the top P 1 . If the velocity of the top v 1 = 2 m/s. Then the ratio of areas A 1 . A 2 is
When a capillary tube is dipped in water, water rises upto 8 cm in the tube. What happens when the tube is pushed down such that its end is only 5 cm above the outside water level
An air bubble of radius 5mm rises through a vat of syrup at a steady speed of 2mm/s. If the syrup has a density of 1 . 4 x 10 3 kg/ m 3 , What is its viscosity ?
A rectangular container contains water to a depth of 50cm and above water there is a 20cm thick layer of oil of specific gravity 0.8. Then pressure of the bottom of container is
A wire having area of cross section 10 − 6 m 2 is stretched to increase its length by 0.1%. Then tension produced is 1000N. Then elastic potential energy stored per unit volume of the wire is
A glass capillary tube is partially dipped in water vertically and water rises to a height h in the tube. The tube is now pushed down so that length of tube above the free surface of water is h/2. Then new angle of contact is
A pump is delivering water through a pipe of cross sectional area 10 cm 2 . If water flows through the pipe with a velocity 4m/s, power output of the pump is
An ideal fluid flows(laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is:
A large tank is partially filled with water. The tank has a small orifice at the bottom and water is coming out of the orifice. When height of water above the orifice is 2 m, rate of flow of water through the orifice is 0.5 m 3 / s . when height of water above the orifice is 0.5 m rate of flow of water through the orifice will be
The potential energy of a molecule on the surface of a liquid compared to one inside the liquid is
A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating, vertically in water at 0 0 C such that its height above the water surface is 20cm. When the temperature of water is increased to 4 0 C , the height of the cylinder above the water surface becomes 21cm. The density of water at T = 4 0 C , relative to the density at T = 0 0 C is close to:
If pressure at half the depth of a lake is equal to 2 3 pressure at the bottom of the lake, then the depth of lake is (Atmospheric pressure = 10 5 N / m 2 )
A balloon filled with Helium gas cannot continue to rise indefinitely. This happens because
When two soap bubbles of radius 3 cm and 6 cm coalesce, the radius of curvature of common surface is
A small spherical droplet of density d is floating exactly half immersed in a liquid of density ρ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet)
A body floats in a liquid of relative density 1.5 with 40% of its volume outside that liquid. If 50% of volume of same body remain in oil, the relative density of oil is
A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 N m – 1 , density = 667 kg m – 3 ) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. Sides of the capillary) make an angle of 60 0 with one another. Then h is close to (g = 10 m s – 2 ).
A small metal sphere falls down in a liquid with terminal velocity when the viscous force on it and its weight are in the ratio 2:5. Then the density of the sphere is
Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :
When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0º, the surface tension of the liquid, in milliNewton m − 1 , is ρ l i q u i d = 900 k g m − 3 , g = 10 m s − 2 (Give answer in closest integer)
A air bubble of radius 1 cm in water has an upward acceleration 9.8 c m s − 2 . The density of water is 1 gm c m − 3 and water offers negligible drag force on the bubble. The mass of the bubble is g = 980 c m / s 2
A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r . If the specific gravity of the shell material is 27 8 w.r.t water, the value of r is:
The blades of a wndmill sweeps out a circle of area 'A'. If the wind flows at a velocity 'v' perpendicular to the circle (denisity of air = ) A) the mass of the air passing through it in time 't' is AV t B) the kinetic energy of the air is C) If the windmill converts 25% of the wind energy into electrical energy and then the electrical power produced is 4.5 kw
A sealed tank containing a liquid of density ρ moves with a horizontal acceleration a, as shown in the figure. The difference in pressure between the points A and B is
A wooden block with a coin placed on its top, floats in water with l as the length immsered and h as the height of water column. After some time the coin falls into water. Then
The tube shown is of uniform cross- section. Liquid flows through it at a constant speed in the direction shown by the arrows . The liquid exerts on the tube
There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to
The force acting tangential to the layers of the liquid is called :
To reduce friction between the moving parts of a machine, the liquid used must have
The main difference between liquid surface and an elastic membrane is
An iron needle slowly placed on the surface of water floats on it because
The order of the thickness of surface film of a liquid is
The sphere of influence of a liquid molecule is completely lying inside the liquid then
A thread is tied slightly loose to a wire frame as in figure and the frame is dropped into a soap solution and taken out. The frame is completely covered with the film. When the portion A is punctured with a pin, the thread
When there are no external forces, the shape of a small liquid drop is determined by
Fig. shows a U-tube of uniform cross-sectional area A accelerated with acceleration a as shown. If d is the separation between the limbs, then the difference in the levels of the liquid in the U-tube is
Air streams horizontally across an aeroplane wing of area 3m 2 weighing 250 kg. The air speed is 60 m/s and 45 m/s over the top surface and under the bottom surface respectively. What is the lift on the wing ? (Density of air 1.293 g/l)
A cylindrical tank of base area A has a small hole of area ‘a’ at its bottom. At the time t = 0, a tap starts to supply water into the tank at the rate of αm 3 /sec. The maximum level of water in the tank is
The terminal velocity of a small ball falling in a viscous liquid depends upon i) its mass m ii) its radius r iii) the coefficient of viscosity of the liquid η and iv) acceleration due to gravity. Which of the following relations is dimensi-onally true for the terminal velocity V =
Water is allowed to flow through a capillary tube of length 10cm and diameter 2 mm under a constant pressure difference of 6.5 cm of water level. If 0.16 litres of water flows in 1 minute, its coefficient of viscosity is,
The length of one edge of a glass plate of thickness 0.2 cm is 9.8 cm. If this edge of the glass plate touches the surface of a liquid of surface tension 60 dyne/cm, then it is pulled down with a force of (Assume that angle of contact to be zero)
A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit.
A candle of diameter d is floating on a liquid in a cylindrical container of diameter D(D>>d) as shown in figure. If it is burning at the rate of 2cm/hour then the top of the candle will
A large block of ice 5 m thick has a vertical hole drilled in it and is floating in a lake. the minimum length of the rope required to draw a bucketfull of water through the hole is (density of ice = 900 kg/m 3 )
In a plant a sucrose solution of coefficient of viscosity 0.0015 N-sm -2 is driven at a velocity of 10 -3 ms -1 through xylem vessels of radius 2 µm and length 5 µm. The hydrostatic pressure difference across the length of xylem vessels in Nm -2 is
Two capillary tubes of same length but different radii r 1 and r 2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the radius of a single tube of same length that can replace the two tubes so that the rate of flow is same as before
A wire of length ‘l’ meters, made of a material of specific gravity 8 is floating horizontally on the surface of water. If it is not wet by water, the maximum diameter of the wire (in milli-meters) upto which it can continue to float is (surface tension of water is T = 70×10 –3 Nm –1 )
A liquid is filled into a semielliptical cross – section with a as semi major axis and b as semi minor axis. The ratio of the surface tension forces on the curved part and the plane part of the tube in vertical position will be
Assume that liquid drop evaporates by decreasing in its surface energy so that its temperature remains unchanged. The surface tension of liquid drop is T, density of liquid is ρ and L is latent heat of vapouration of liquid. What should be the minimum radius of the drop for this to be possible
Equal volumes of two non viscous incompressible and immiscible liquids of densities ρ 1 and ρ 2 and are poured into two limbs of a circular tube of radius R kept vertical such that half of the tube is filled with liquid. The angular position of interface from vertical is
Glycerine flows steadily through a horizontal tube of length 1.5m and radius 1.0cm. If the amount of glycerine collected per second at one end is 4.0 x 10 – 3 K g S – 1 , what is the pressure difference between the two ends of the tube? Density of glycerine = 1.3 x 10 3 K g m – 1 and viscosity of glycerine = 0.83 Ns m – 2 (You may also like to check if the assumption of laminar flow in the tube is correct.)
A cylindrical drum, open at the top, contains 30 liters of water. It drains out through a small opening at the bottom. 10 liters of water comes out in time t 1 , the next 10 liters in further time t 2 and the last 10 liters in further time t 3 . Then,
The property of viscosity in gas is due to
A liquid of density ρ comes out with a velocity V from a horizontal tube of area of cross – section A fitted at the bottom of a large tank. The reaction force exerted by the liquid on the tube is F. a) F ∝ V b) F ∝ V 2 c) F ∝ A d) F ∝ ρ
By inserting a capillary tube upto a depth l in water, a capillary rise h is observed in the tube. If the lower end of the capillary tube is closed inside water and the capillary is taken out and closed end opened , to what height the water will remain in the tube when l > h
An aluminium sphere is dipped into water at 10°C. If the temperature is increased, the force of buoyancy
A small stone is inside a ice block which floats in water. When the ice fully melts the level water
An empty cylindrical container, open at the top is floating in water with its axis vertical with 50% of its volume submerged in water. Wall of the container is very thin. Now water is poured in the cylinder so as to fill 25% of its volume. What fraction of the volume of the container will be submerged in water now?
Pressure inside a soap bubble, formed in vacuum is P. When this bubble in taken in a closed chamber filled with gas at pressure P/2, its radius is reduced to half of its initial value. Now the pressure inside the bubble will be
The work done in increasing the size of a soap film from 10 cm × 6 cm to 10 cm × 11 cm is 3 × 10 – 4 Joule. The surface tension of the film is
Assertion : A ship floats higher in the water on a high pressure day than on a low pressure day. Reason : Floating of ship in the water is not possible because of buoyancy force which is present due to pressure difference.
Assertion : Surface tension decreases with increase in temperature. Reason : On increasing temperature kinetic energy increases and inermolecular forces decreases.
Assertion : A large soap bubble expands while a small bubble shrinks, when they are connected to each other by a capillary tube. Reason : The excess pressure inside bubble (or drop) is inversely proportional to the radius.
When the temperature is increased the angle of contact of a liquid
Statement I : The angle of contact of a liquid with a solid increases with increase in temperature of liquid. Statement II : With increase in temperature, the surface tension of the liquid increases.
Statement I :A large force is required to draw apart normally two glass plates enclosing a thin water film. Statement II : Water works as glue and sticks two glass plates.
The wettability of a surface by a liquid depends primarily on
Statement I : At critical temperature, surface tension of a liquid becomes zero. Statement II : At critical temperature, intermolecular forces for liquids and gases become equal. Liquid can expand without any restriction.
Statement I : It is easier to spray water in which some soap is dissolved. Statement II : Soap is easier to spread.
Statement I : A solid sphere placed in the fluid under high pressure is compressed uniformly on all sides. Statement II : The volume of solid sphere will decrease with change of its geometrical shape.
When the lower end of a vertical capillary tube of radius r is dipped in water, water rises in it due to capillarity action and change in gravitational potential energy of water is U. If the tube is replaced by another tube of radius 2r, charge in gravitational potential energy will be
A thin spherical shell is rolling without slipping on a horizontal surface. If K R and K T respectively represent kinetic energy due to rotational motion and kinetic energy due to translational motion, then K R K T is
Scent sprayer is based on
By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg(density = 13.6 g / cm 3 ). Using the straw, he can drink water from a glass up to a maximum depth of (atmospheric pressure is 760 mm of Hg)
A wide cylindrical tank with a small opening in the bottom has a water column of height h 1 and density d. Above the water column, there is a layer of kerosene oil of thickness h 2 and density 0.8d. The velocity of efflux through the opening is
Bernoulli’s principle is based on the law of conservation of
We have two different liquids A and B whose relative densities are 0.75 and 1.0 respectively. If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
A man is sitting in a boat which is floating in a pond. If the man drinks some water from the pond, the level of water in the pond
Assertion : Bernoulli’s equation holds for non-steady or turbulent flows. Reason : In these situations, velocity and pressure are constant with time.
Statement I : Aeroplanes are made to run on the runway before take off, so that they acquire the necessary lift. Statement II : Lift of aeroplane is based on Bernoulli’s theorem.
Statement I : If an object is submerged in fluid at rest, the fluid exerts a force on its surface. Statement II : The force exerted by the fluid at rest has to be parallel to the surface in contact with it.
Statement I : The velocity increases, when water flowing in broader pipe enter a narrow pipe. Statement II : According to equation of continuity, product of area and velocity is constant.
Statement I : A fluid flowing out of a small hole in a vessel apply a backward thrust on the vessel. Statement II : According to equation of continuity, the product of area and velocity remain constant.
Statement I : Liquids and gases are largely incompressible and densities are therefore, nearly constant at all pressures. Statement II : Liquids exhibit a large variation in densities with pressure but gases do not.
Statement I : A spinning cricket ball deviates from its trajectory as it moves through air. Statement II : While spinning the ball is moving forward and relative to it the air is moving backward.
Statement I : The flow of fluid is said to be steady if at any given point, the velocity of each passing fluid particle remains constant. Statement II : The path taken by a fluid particle under a steady flow is a streamline.
Statement I : The flow is turbulent for Reynolds number greater than 2000. Statement II : Turbulence dissipates kinetic energy in the form of heat.
Statement I : Sudden fall of pressure at a place indicates storm. Statement II : Air flows from higher pressure to lower pressure.
Statement I : Pascal law is the working principle of hydraulic lift. Statement II : Pressure = thrust area
Statement I : A dam for water reservoir is built thicker at bottom than at the top. Statement II : Pressure of water is very large at the bottom.
Statement I : The velocity of flow of liquid is smaller when pressure is larger and vice versa Statement II : According to Bernoulli’ s theorem, for the stream line flow of an ideal liquid, the total energy per unit mass remains constant.
Consider ideal flow of water through a pipe with its axis horizontal. A and B are the two points in the pipe at the same horizontal level(A lies on the upstream), then
A water tank of height 10 m, completely filled with water is placed on a level ground. It has two holes one at 3m and the other at 7 m form its base. The water ejecting from
If two ping-pong balls are suspended near each other and a fast stream of air is produced in the space between the balls, then the ball
In old age arteries carrying blood in the human body become narrow resulting in an increase in the blood pressure. This follows from
If air is blown under one of the pans of a physical balance in equilibrium, then the pan will
A pump is delivering water at a rate of 0.05 m 3 / s through a pipe of cross-sectional area 10 c m 2 . Ignoring all losses, find the power of the pump.
A liquid drop of radius R is broken into 1000 drops each of radius r. If T is surface tension, change in surface energy is
Streamline flow is more likely for liquids with
A water drop is divided into 8 equal droplets. The pressure difference between inner and outer sides of the big drop
A spherical liquid drop of radius R is divided into eight equal droplets. If the surface tension is T, then the work done in this process will be
A metallic sphere of radius 1 . 0 × 10 – 3 m and density 1 . 0 × 10 4 kg / m 3 enter a tank of water, after a free fall through a distance of h in the earth’s gravitational field, if its velocity remains unchanged after entering water, determine the value of h. Given: coefficient of viscosity of water = 1 . 0 × 10 – 3 N – s / m 2 , g = 10 m / s 2 and density of water = 1 . 0 × 10 3 kg / m 3 .
A drop of water of radius 0.0015 mm is falling in air. If the coefficient of viscosity of air is 1.8 × 10 – 5 kg / ( m / s ) , what will be the terminal velocity of the drop? (density of water = 1 . 0 × 10 3 kg / m 2 and g = 9 . 8 m / s 2 ) Density of air can be neglected.
An air bubble of 1 cm radius is rising at a steady rate of 2.00 mm s – 1 through a liquid of density 1 . 5 g cm – 3 . Neglect density of air. If g = 1000 cm s – 2 , then the coefficient of viscosity of the liquid is
Two identical spherical drops of water are falling (vertically downwards) through air with a steady velocity of 5 cm/sec. If both the drops coalsece (combine) to form a new spherical drop, the terminal velocity of the new drop will be (neglect buoyant force on the drops).
Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is
A capillary tube of length l = 50 cm and radius r = 1 4 mm is immersed vertically into water. Find the capillary rise if angle of contact = 0 0 and coefficient of surface tension = 72 dyne/cm. (Take g = 1000 cm / s 2 ).
A capillary tube of length l = 50 cm and radius r = 1 4 mm is immersed vertically into water. Find the capillary rise if angle of contact = 0 0 and coefficient of surface tension = 72 dyne/cm. (Take g = 1000 cm / s 2 ).
The thickness of the ice layer on the surface of lake is 20 m. A hole is made in the ice layer. What is the minimum length of the rope required to take a bucket full of water out? (Take density of ice = 0.9×10 3 kg / m 3 )
A rectangular block is 5 cm × 5 cm × 10 cm in size. The block floating in water with 5 cm side vertical. If it floats with 10 cm side vertical, what change will occur in the level of water?
A body is just floating in a liquid (their densities are equal). If the body is slightly pressed down and released it will:
A cork ball is floating on the surface of water in a beaker. The beaker is covered with a bell jar and the air is evacuated. What will happen to the ball?
A steel ball is floating in a trough of mercury. If we fill the empty part of the trough with water, what will happen to the steel ball?
A piece of ice is floating in a beaker containing water. When ice melts, the temperature falls from 20 0 C to 4 0 C and the level of water:
A boy is carrying a bucket of water in one hand and a piece of plastic in the other. After transferring the plastic piece to the bucket(in which it floats the boy will carry:
A bird resting on the floor of an airtight box which is being carried by a boy starts flying. The boy will fell that the box is now:
A wooden block is floating in a water tank. The block is pressed to its bottom. During the process, work done is equal to:
A solids floats submerged in a liquid. When the liquid is heated, which of the following is most likely to happen?
A log of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sink should be (density of wood = 600 kg/ m 3 )
A tank has a hole at its bottom. The time needed to empty the tank from level h 1 to h 2 will be proportional to
A neckless weighing 50 gm in air, but it weighs 46 g in water. Assume copper is mixed with gold to prepare the neckless. Find how much copper is present in it. (Specific gravity of gold is 20 and that of copper is 10).
An aircraft of mass 4 × 10 5 kg with total wing are m 2 in level flight at a speed of 720 km h – 1 . The density of air at its height is 1 . 2 kg m – 3 . The fractional increase in the speed of the air on the upper surface of its wings relative to the lower surface is (Take g = 10 ms – 2 )
Two syringes of different cross section (without needle) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are 1 cm and 3 cm respectively. If a force of 10 N is applied to the smaller piston then the force exerted on the larger piston is
The fraction of a floating object of volume V o and density d o above the surface of a liquid of density d will be
When a loaded test tube floats vertically with 1 3 and 1 4 of the lengths inside two liquids, then the ratio of the densities of the two liquids is
Two solid pieces, one of gold and the other of silver when immersed completely in water have equal weighs. When weighed in air
A boat having a length of 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is (density of water = 1000 kg/ m 3 )
A liquid of density 800 kg m – 3 is filled in a tank open at the top. The pressure, of the liquid, at the bottom of the tank is 6.4 atmospheres. The velocity of efflux through a hole at the bottom is (1 atmosphere = 10 5 N m – 2 )
A long cylindrical tank of radius 1 m is being filled by a pipe of radius 2 cm. The incoming water has a velocity of 1 m/s, The tank has a hole of radius 1 cm at the bottom. What is the height of water in the tank in steady state?
There is a hole in the bottom of tank having water. If total pressure at bottom is 2 atm ( 1 atm = 10 5 N / m 2 ) then the velocity of water flowing from hole is
A body weights 150 kg in air, 120 g in water and 130 g in a liquid. The density of liquid in g cm – 3 is
A body of density d and volume V floats with volume V 1 of its total volume V immersed in a liquid of density d 1 and the rest of the volume V 2 immersed in another liquid of density d 2 ( < d 1 ) . The volume V 1 immersed in liquid of density d 1 is
Two solids A and B float in water. It is observed that A floats with half of its volume immersed and B floats with 2 3 of its volume immersed. The ratio of densities of A and B is
A U-tube containing a liquid is accelerated horizontally with a constant acceleration a. If the separation between the two vertical limbs is l, then the difference in the heights of the liquid in the two arms is:
The diameter of the piston of a hydraulic automobile is D metre. What pressure, in atmosphere is required to lift a car of mass m kg?
In a hydraulic lift at a service station, the radii of the large and small piston are in the ratio of 20 : 1. What weight placed on the small piston will be sufficient to lift a car of mass 1200 kg?
A uniformly tapering vessel of height h whose lower and upper radii are r and R is completely filled with a liquid of density ρ . The forces that acts on the base of the vessel due of the liquid is
V 1 is the terminal velocity of a metal sphere of mass 0.5 gm and density 5 gm/cc when it is falling in water. V 2 is the terminal velocity of another metal sphere of mass 4 gm and density 9 gm/cc when it is falling in water. The ratio of V 1 and V 2 .
A body is floating in oil of density 0.8 g m / c m 3 with 50% of its volume submerged in the oil. What percent of its volume will remain above the water srface when the body floats in water?
30 N horizontal force is required to pull a plate of area 1 m 2 with constant velocity of 2 m/s over a thin film of oil of thickness 0.25mm, then viscosity of the oil in N − S / m 2 , is
We have two different liquids A and B whose specific gravities are 0.75 and 1.0 respectively. If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids then
8 identical drops of water, each of radius 1 mm coalesce to form a single drop. Then heat generated in the process is [surface tension of water is 0.072 N/m]
A tank is filled with water to a height H. The tank has two orifices A and B at depths H/4 and H/2 respectively below the free surface of water. Area of orifices A and B are respectively ‘a’ and ‘a/2’. If Q A and Q B represent rate of volume flow of water through A and B, then Q A / Q B is
An orifice is present on the vertical wall of a water tank at a depth h below the free surface of water. When h = 4m, rate of flow of water through the orifice is 0.25 m 3 s . What will be the rate of flow of water when h = 9m?
Assume the density of brass weights to be 8 g cm – 3 and that of air to be 0.0012 g cm – 3 . What fractional error arises from neglecting buoyancy of air in weighing and object of density 3.4 g cm – l on a beam balance?
Spheres of iron and lead having same mass are completely immersed in water. Density of lead is more than that of iron. Apparent loss of weight is W 1 for iron sphere and W 2 for lead sphere. Then W 1 / W 2 is
Column Ishows the Bernoulli’s equation in the different forms. Column II lists certain units each of which pertains to one of the possible forms of the equation. Column I Column II i. v 2 2 g + p ρg + z = constant p. Total energy per unit mass ii. ρV 2 2 + P + ρ gz = constant q. Total energy per unit weight iii. V 2 2 + P ρ + gz = constant r. Total energy per unit volume (where z is ratio of height to volume) Now match the given columns and select the correct option from the codes given below.
A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes T 1 time to decrease the height of water H η ( η > 1 ) ; and it takes T 2 time to take out the rest of water. If T 1 = T 2 , then the value of η is
A piece of brass (Cu and Zn) weighs 12.9 g in air. When completely immersed in water, it weighs 11.3g. Then relative densities of Cu and Zn are 8.9 and 7.1 respectively. The mass of copper in the alloy is
A 0.5 kg block of brass (density; 8 x 10 3 kg m – 3 ) is suspended from a string. What is the tension in the string if the block is completely immersed in water? (g = l0 ms – 2 )?
A raft of wood (density 600 kg/ m 3 ) of mass 150 kg floats in water. How much weight can be put on the raft to make it just sink?
Two solids A and B float in water. It is observed that A floats with 1 3 of its volume immersed and B floats with 3 4 of its volume immersed. The ratio of densities of A and B is
A metal block having an internal cavity weight 110 g in air and 80 g in water. If the density of metal is 5.5 g/cc, then the volume of cavity is:
A glass beaker of mass 400 g floats in water with the open end just touching the surface of water and half of the beaker filled with water. The inner volume of the beaker is 500 c m 3 . What is the density of the material of the beaker?
A tank 5 m high is half filled with water and then is filled to the top with oil of density 0.85 g / cm 3 . The pressure at the bottom of the tank, due to these liquids is
A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be
A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the. sphere now sinks into the water
A cylindrical tank has a hole of 1 cm 2 in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 70 cm 3 /s, then the maximum height up to which water can rise in the tank is
A ball of radius r and density ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is η , the value of h is given by
A homogeneous solid cylinder of length L(L > H/2). Cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure P 0 . Then density D of solid is given by
A vessel contains oil (density: 0.8 gm/cm 3 ) over mercury (density: 13.6 gm/cm 3 ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm 3 is
A U-tube in which the cross-sectional area of the limb on the left is one quarter, the limb on the right contains mercury (density 13.6 g/cm 3 ). The level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?
A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is
Water is filled in a cylindrical container to a height of 3 m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1 . The square of the speed of the liquid coming out from the orifice is (g = 10 m/s 2 )
Figure shows four containers of olive oil. The pressure at depth h is
A smooth gate is kept in equilibrium by applying a horizontal force. What is the value of y so that no horizontal reaction force acts at the pivot?
A uniformly tapering vessel is filled with a liquid of density 900 kg/m 3 . The force that acts on the base of the vessel due to the liquid is g = 10 ms − 2
A vertical U-tube of uniform cross-section contains mercury in both sides of its arms as shown below. Glycerin column of 10 cm is introduced into one of its arms. Oil of density 0.8 g/cc is poured into the other arm until the upper surface of the oil and glycerin are at the same horizontal level. ρ Hg = 13.6 g / cc , ρ glycerine = 1.3 g / cc The length of oil column is
A block of wood is floating in water in a closed vessel as shown in the figure. The vessel is connected to an air Pump. When more air is pushed into the vessel, the block of wood floats with (neglect compressibility of water)
A closed rectangular vessel completely filled with a liquid of density ρ moves with an acceleration a = g. The value of the pressure difference at point A and B i.e., (P 1 – P 2 ) is
When at rest, a liquid stands at the same level in the tubes as shown in the figure. But as indicated, a height difference h occurs when the system is given an acceleration a towards the right. Then h is equal to
A sealed tank containing a liquid of density ρ moves with horizontal acceleration a as shown in the figure. The difference in pressure between two points A and B will be
Water rises to a height of 2 cm in a capillary tube. If the tube is tilted 60 0 from the vertical, water will rise in the tube to a length of
A vessel contains oil (density = 0.8 g/cm 3 ) over mercury (density = 13 .6 g/cm 3 ). A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of sphere in g/cm 3 is
A cylindrical block is floating (partially submerged) in a vessel containing water. Initially, the platform on which the vessel is mounted is at rest. Now the platform along with the vessel is allowed to fall freely under gravity. As a result, the buoyancy force
A beaker containing water is placed on the platform of a spring balance. The balance reads 1.5 kg. A stone of mass 0.5 kg and density 10 4 kg/m 3 is immersed in water without touching the walls of the beaker. What will be the balance reading now?
A solid uniform ball of volume V floats on the interface of two immiscible liquids (see the figure). The specific gravity of the upper liquid H 2 O is ρ 1 and that of lower one H g is ρ 2 and the specific gravity of ball is ρ ( ρ 1 < ρ < ρ 2 ) . The fraction of the volume of the ball in the upper liquid is
An ideal fluid flows in the pipe as shown in the figure. The pressure in the fluid at the bottom P 2 is the same as it is at the top P 1 . If the velocity of the top v 1 = 2 m/s. Then the ratio of areas A 1 :A 2 is
A hole is made at the bottom of a tank filled with water (density= 10 3 kg/m 3 ). If the total pressure at the bottom of the tank is 3 atm (1 atm = 10 5 N/m 2 ), then the velocity of efflux is
A cylindrical vessel contains a liquid of density ρ up to height h. The liquid is closed by a piston of mass m and area of cross section A. There is a small hole at the bottom of the vessel. The speed v with which the liquid comes out of the hole is
In a cylindrical water tank there are two small holes Q and P on the wall at a depth of h 1 from the upper level of water and at a height of h 2 from the lower end of the tank, respectively, as shown in the figure. Water coming out from both the holes strike the ground at the same point. The ratio of h 1 and h 2 is
A pitot tube is shown in figure. Wind blows in the direction shown. Air at inlet A is brought to rest, whereas its speed just outside of opening B is unchanged. The U tube contains mercury of density ρ m . Find the speed of wind with respect to Pitot tube. Neglect the height difference between A and B and take the density of air as ρ a
Two holes are made in the side of the tank such that the jets of water flowing out of them meet at the same point on the ground. If one hole is at a height of 5 cm above the bottom, then the distance of the other hole from the top surface of water is
If T is surface tension of soap solution, the amount of work done in blowing a soap bubble from a diameter D to a diameter 2D is
A water drop is divided into eight equal droplets. The pressure difference between inner and outer sides of the big drop
Two soap bubbles, one of radius 50 mm and the other of radius 80 mm, are brought in contact so that they have a common interface. The radius of the curvature of the common interface is
A glass rod of radius r 1 is inserted symmetrically into a vertical capillary tube of radius r 2 such that their lower ends are at the same level. The arrangement is now dipped in water. The height to which water will rise into the tube will be ( σ – surface tension of water ρ – density of water)
Work W is required to form a bubble of volume V from a given solution. What amount of work is required to be done to form a bubble of volume 2V?
The surface energy of a liquid drop is E. It is sprayed into 1000 equal droplets. Then its surface energy becomes
A marble of mass x and diameter 2r is gently released in a tall cylinder containing honey. If the marble displaces mass y (< x) of the liquid, then the terminal velocity is proportional to
A sphere of brass released in a long liquid column attains a terminal speed v 0 . If the terminal speed is attained by a sphere of marble of the same radius and released in the same liquid is nv 0 , then the value of n will be (Given: The specific gravities of brass, marble and liquid are 8.5 , 2.5 and 0.8 respectively)
Between a plate of area 100 cm 2 and another plate of area 100 cm 2 there is a 1 mm, thick layer of water. If the coefficient of viscosity of water is 0.01 poise, then the force required to move the smaller plate with a velocity 10 cms -1 with reference to large plate is
A river 10 m deep is flowing at 5 ms -1 . The shearing stress between horizontal layers of the river it ( η = 10 − 3 SI units)
A spherical ball falls through viscous medium with terminal velocity v. If this ball is replaced by another ball of the same mass but half the radius, then the terminal velocity will be (neglect the effect of buoyancy.)
A solid sphere falls with a terminal velocity of 20 ms -1 in air. If it is allowed to fall in vacuum,
Water rises to a height h in a capillary tube of cross-sectional area A. The height to which water will rise in a capillary tube of cross-sectional area 4A will be
Equal masses of water and a liquid of density 2 are mixed together; then the mixture has a density of:
Pressure at a point inside a liquid does not depend on:
A vessel contains liquid of density ρ as shown in Fig. The gauge pressure at the point P is:
Two stretched membranes of area 2 cm 2 and 3 cm 2 are placed in a liquid at the same depth. The ratio of the pressure on them is:
Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by:
Pressure is applied to an enclosed fluid. It is:
The principle of operation of a Brahma’s press is based on:
A piston of cross-sectional area 100 cm 2 is used in a hydraulic press to exert a force of 10 7 dyne on the water. The cross-sectional area of the other piston which supports an object having a mass 2000 kg is:
The pressure of water at bottom in a lake is 3 2 times that at 2 half depth where the water barometer reads 10 m. The depth of the lake is:
The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to:
Two identical cylindrical vessels with their bases at the same level each contains a liquid of density d. The height of the liquid in one vessel is h 1 and that in the other vessel is h 2. The area of either base is A. The work done by gravity in equalising the levels, when the two vessels are connected is:
The limbs of a glass U – tube are lowered into vessels A and B, A containing water. Some air is pumped out through the top of the tube C. The liquids in the left hand limb A and the right hand limb B rise to heights of 10 cm and 12 cm respectively. The density of liquid B is:
Pressure at the bottom of tank of water is 3P, where P is atmospheric pressure. If the water is drawn out till the level of water is lowered by one-fifth, then the pressure at the bottom of the tank is:
By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg (density = 13.6 g/ cm).Using the straw, he can drink water from a glass up to a maximum depth of:
An open U-tube contains mercury. When 11.2 cm of water is poured into one of the arms of the tube, how high does the mercury rise in the other arm from its initial level?
The neck and bottom of a bottle are 3 cm and 15 cm in radius respectively. If the cork is pressed with a force 12 N in the neck of the bottle, then force exerted on the bottom of the bottle is:
A uniformly tapering vessel is filled with a liquid of density 900 kg/m 3 . The force that acts on the base of the vessel due to the liquid is: (g = 10 m/s 2 )
Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ , the surface tension of water is T and the atmospheric pressure is P 0 . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude:
Radius of one arm of hydraulic lift is four times of radius of other arm. What force should be applied on the narrow arm to lift 100 kg?
A U-tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is:
Two pieces of metal when immersed in a liquid have equal upthrust on them; then:
When a body is wholly or partially immersed in a liquid it appears to lose weight. This loss of weight is equal to the weight of:
If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect?
A body floats in a liquid contained in a beaker. The whole system as shown in Fig.(B) falls freely under gravity. The upthrust on the body due to the liquid is:
A hydrogen balloon released on the moon would:
An iron ball is weighed in air and then in water by a spring balance :
A block of metal ( density 7 g/cc) of size 5 cm x 5 cm x 5 cm is weighed completely submerged in water. What will be its apparent weight (density of water = 1 g/cc)?
A glass bulb is balanced by a brass weight in a sensitive beam balance. Now the balance is covered by a bell-jar which is then evacuated; then:
A weightless rubber balloon has 100 g of water in it. Its weight in water will be:
The reading of a spring balance when a block is suspended from it in air is 60 N. This reading is changed to 40 N when the block is submerged in water. The specific gravity of the block must therefore be:
A vessel with water is placed on a weighing pan and reads 600 g. Now a ball of 40 g and density 0.80 g/cc is sunk into the water with a pin as shown in fig. keeping it sunk.The weighing pan will show a reading:
Two bodies with volumes V and 2 V are equalized on a balance. The larger body is then immersed in oil of density d 1 = 0.9 g/cm 3 while the smaller body is immersed in another liquid when it is found that the equilibrium of the balance is not disturbed. The density of the second liquid is then:
A body of weight W 1 displaces an amount of water W 2 . When floating:
When a ship floats on water:
A wooden cylinder floats vertically in water with half of its length immersed. The density of wood is:
Two solids A and B float in a liquid. It is observed that A floats with half its volume immersed and B floats with (2/3) of its volume immersed. Compare the densities of A and B:
A body floats with (1/3) of its volume outside water and (3/4) of its volume outside another liquid. The density of the other liquid is:
A common hydrometer reads specific gravity of liquids. Compared to the mark 1.6 on the stem, the mark 1.5 will be:
When a loaded boat enters into the sea from a river, it rises because:
A raft of wood (density 600 g/m 3 ) of mass 120 kg floats in water. How much weight can be put on the raft to make it just sink?
It is easier to swim in sea water than in river water because:
A cubical block of wood of side a and density ρ floats in water of density 2 ρ . The lower surface of the cube just touches the free end of a massless spring of force constant k fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is
A hollow sphere has a small hole in it. On lowering the sphere in a tank of water, it is observed that water enters into the hollow sphere at a depth of 40 cm below the surface. Surface tension of water is 7 x 10 -2 N/m. The diameter of the hole is
Two soap bubbles of radii a and b combine to form a single bubble of radius c. If P is the external pressure, then the surface tension of the soap solution is
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
A thin square plate of side 5 cm is suspended vertically from a balance so that lower side just dips into water with side to surface. When the plate is clean ( θ :0 o ), it appears to weigh 0.044 N. But when the plate is greasy ( θ =180 o ), it appears to weigh 0.03 N. The surface tension of water is
A uniform rod OB of length 1 m, cross-sectional area 0.012 m 2 and relative density 2.0 is free to rotate about O in vertical plane. The rod is held with a horizontal string AB which can withstand a maximum tension of 45 N. The rod and string system is kept in water as shown in figure. The maximum value of angle α which the rod can make with vertical without breaking the string is
Figure shows a closed container completely filled with an ideal liquid of density ρ .In the liquid there is a spherical body of volume V and density σ attached to a string whose other end is attached to the roof of the container. The container is accelerating with an acceleration ‘a’ towards right. The force exerted by the liquid on the spherical body when it is in equilibrium with respect to the liquid, will be:
A thin plate AB of large area A is placed symmetrically in a small gap of height ‘h’ filled with water of viscosity η 0 and the plate has a constant velocity v by applying a force F, as shown in the figure. If the gap is filled with some other liquid of viscosity 0.75 η 0 where should the plate be placed in the gap, so that the plate can again be pulled at the same constant velocity V, by applying the same force F. (Take h = 20 cm)
A cube of wood of mass 0.5 kg and density 800 kg m -3 is fastened to the free end of a vertical spring of spring constant k= 50Nm -1 , fixed at the bottom. Now, the entire system is completely submerged in water. The elongation or compression of the spring in equilibrium is β 2 cm. The value of β is . (Given, g= 10 ms -2 )
For the arrangement shown in the figure, Area of the cross section of the tank A = 5 m 2 and area of the orifice a = 4 cm 2 . If the time interval in seconds after which the water jet ceases to cross the wall is Nx10 3 sec. The value of N is . [Assume that the container remaining fixed]
A plate of area 2 m 2 is made to move horizontally with a speed of 2 ms -1 by applying a horizontal tangential force over the free surface of a liquid. The depth of the liquid is 1 m and the liquid in contact with the bed is stationary. Coefficient of viscosity of liquid = 0.01 poise. The tangential force needed to move the plate is α x 10 -3 N. The valve of α is .
A hole of area 5 cm 2 is formed in the side of a ship 3 m below the water level. What minimum force (in N) is required to hold on a patch covering the hole from the inside of the ship?
An aluminium wire is wound on a piece of cork of mass 10 g. The densities ρ c , ρ a a n d ρ w of cork, aluminium and water are 0 . 5 × 10 3 kg / m 3 , 2 . 7 × 10 3 kg / m 3 and 1 × 10 3 kg / m 3 respectively. The minimum mass of aluminium wire that should be wound on the cork so that the cork with the wire should stay completely submerged in water is:
Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross-sectional area 10 -6 m 2 .The breaking stress of the wire is 7 x 10 6 N/m 2 . The block is placed in a beaker of base area 200 cm 2 and initially i.e. at t=0, the top surface of water and the block coincide. There is a pump at the bottom corner which ejects 2 cm 3 of water per sec. If the time at which the wire will break is N x 10 2 sec. The value of N is .
A metal ball of density 7800 kg/m 3 is suspected to have a large number of inner cavities. It weighs 9.8 kg when weighed directly on a balance and 1.5 kg less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately:
A square plate of 1 m side moves parallel to a second plate with velocity 4 m/s. A thin layer of water exists between plates. If the viscous force is 0.002N and the coefficient of viscosity is 0.01 poise then find the distance between the plates in m.
The drawing shows a hydraulic chamber with a spring (spring constant: 1600 N/m) attached to the input piston and a rock of mass 40.0 kg resting on the output plunger. The piston and plunger are nearly at the same height, and each has a negligible mass. By how much is the spring compressed (in cm) from its unstrained position?
A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D >> d) as shown in figure. If it is burnin g at the rate of 2 cm/hour then the top of the candle will; (assume that density of wax is half the density of the liquid)
A solid sphere of volume v and density ρ floats at the interface of two immiscible liquids of densities ρ 1 and ρ 2 respectively. If ρ 1 < ρ < ρ 2 , then the ratio of volume.of the parts of the sphere in upper and lower liquid is:
When air of density 1.3 kg/m 3 flows across the top of the tube shown in the accompanying figure, water rises in the tube to a height of 1.0 cm. The speed of the air (in m/s) is
A solid block of volume V = 10 -3 m 3 and density d = 800 kg/m 3 is tied to one end of a string, the other end of which is tied to the bottom of the vessel. The vessel contains 2 immiscible liquids of densities ρ 1 = 1000 kg/m 3 and ρ 2 = 1500 kg/m 3 . The solid block is immersed with 2/5th of its volume in the liquid of higher density and 3/5th in the liquid of lower density. The vessel is placed in an elevator which is moving up with an acceleration of a=g/2. The tension in the string is . [g = 10 m/s 2 ]
The diagram shows Venturi meter through which water is flowing. The speed of water at X is 2 cm/sec. The speed of water at Y in cm/s (taking g=1000 cm/sec 2 ) is
An ice block floats in a liquid whose density is less than water. A part of block is outside the liquid. When whole of ice has melted, the liquid level wil1:
When a body is weighed in a liquid the loss in its weight is equal to: (i) weight of liquid displaced by the body (ii) weight of water displaced by the body (iii) the difference in weights of body in air and liquid (iv) the upthrust of liquid on the body
A piece of wood is floating in water kept in a bottle. The bottle is connected to an air pump. When more air is pushed into the bottle from the pump: (i) the wood piece will rise a little up (ii) the thrust of air will increase (iii) the thrust of water will decrease (iv) the total thrust will remain unchanged
Water is flowing through a pipe of uniform cross-section under constant pressure. At some place the pipe becomes narrow; the pressure of water at this place:
An incompressible non-viscous fluid flows steadily through a cylindrical pipe which has radius 2R at point A and radius R at point B farther along the flow direction. If the velocity at point A is V, its velocity at point B will be:
For the system shown in the figure, the cylinder on the left at L has a mass of 600 kg and a cross-sectional area of 800 cm 2 .The piston on the right, at S, has cross-sectional area 25 cm 2 and negligible weight. If the apparatus is filled with oil ρ = 0.75 g / cm 3 . The force F (in N) required to hold the system in equilibrium is . Take g= 10 m/s 2 .
In a vessel of water a hole is made at a depth of 3 .5 m from the free surface. The velocity of efflux will be:
The volume of a liquid flowing per sec out of an orifice at the bottom of a tank does not depend upon:
A tank is filled with water to a height H. A hole is made in one of the walls at a depth D below the water surface. The distance x from the foot of the wall at which the stream coming out of the tank strikes the ground is given by:
A gale blows over a house. The force due to the gale on the roof is:
An aeroplane works on:
Magnus effect is very near to the:
A tube of uniform cross-section has two vertical portions connected with a horizontal thin tube 8 cm long at their lower ends. Enough water to occupy 22 cm of the tube is poured into one branch and enough oil of specific gravity 0.8 to occupy 22 cm is poured into the other. Find the distance (in cm) of the common surface E of the two liquids from point B.
A horizortal-oriented tube AB of length l :2.5 m rotates with a constant angular velocity ω = 5 rad/s about a stationary vertical axis OO’ passing through the end A (figure). Initially the tube is filled with an ideal fluid. The end A of the tube is open, the closed end B has a very small orifice. Find the velocity of the fluid (in m/s) relative to the tube when the liquid column length in tube reduces to h=1 m.
A solid block owf volume V=10 -3 m 3 and density d – 800 kg/m 3 is tied to one end of a string, the other end of which is tied to the bottom of the vessel. The vessel contains 2 immiscible liquids of densities ρ 1 =1000 kg/m 3 and ρ 2 =1500 kg/m 3 . The solid block is immersed with 2/5th of its volume in the liquid of higher density and 3/5th in the liquid of lower density. The vessel is placed in an elevator which is moving up with an acceleration of a = g/2. The tension in the string (in N) is . (g = 10 m/s 2 )
To get the maximum flight, a ball must be thrown as:
A cork is submerged in water by a spring attached to the bottom of a pail. When the pail is kept in an elevator moving with acceleration downwards. The length of spring:
Water falling vertically from the mouth of a tap in streamline flow forms a tapering column as shown in the Fig. 12.69. Which of the following is the most correct explanation for this?
The outboard motor of a small boat has a propeller of diameter 200 mm. When the boat is at rest, the propeller sends back a stream of water at a speed of 10 m/s. One-half of the work that is being done by the motor is transferred to this water as kinetic energy. The power output of the motor is ( density of water is 1000 kg/m 3 ) :
A container having a hole at the bottom is free to move on a horizontal surface. As the liquid comes out, the container with an acceleration α and finally acquires a velocity v ( when the liquid has drained out). Neglect the mass of container. The correct option out of the following is:
At what speed, the velocity head of water is equal to pressure head of 40 cm of Hg?
A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m s – 1 ) through a small hole on the side wall of the cylinder near its bottom is:
Bernoulli’s equation is a consequence of conservation of:
In old age arteries carrying blood in the human body become narrow resulting in an increase in the blood pressure. This follows from :
Water from a tap emerges vertically downwards with an initial speed of 1.0 m s -1 . The cross-sectional area of the tap is 10 -4 m 2 . Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is:
A cylindrical tank is placed on a platform 5 m high. Initially the tank is filled with water up to a height 5 m. An orifice is made in the side wall of tank just at the bottom. Speed with which water coming out of the orifice hits ground is nearly: (take g = 10 m/s 2 )
An L-shaped tube with a small orifice is held in a water stream as shown in Fig. The upper end of the tube is 10.6 cm above the surface of water. What will be the height of the jet of water coming from the orifice? Velocity of water stream is 2.45 m/s :
Water flows at a speed of 6 cms –1 through a tube of radius 1cm. Coefficient of viscosity of water at room temperature is 0.01 poise . The Reynold number is
16cc of water flows per second through a capillary tube of radius a cm and length l cm when connected to a pressure head h cm of water. If a tube of same length and radius (a/2) cm is connected to the same pressure head, the quantity of water flowing through the second tube will be (in cc)
A uniform rectangular plate is hanging vertically downward from a hinge that passes along its left edge. By blowing air at 12m/s over the top of the plate only, it is possible to keep the plate in a horizontal position, as illustrated in part (a) of the drawing. To what value of speed (in m/s) should the air be blown so that the plate is kept at 30 ∘ angle with respect to the vertical, as in part (b) of the drawing? (assume the velocity beneath the plate is almost zero)
A heavy load W is supported on a platform of area S by applying a force F on a small piston of area S / 10 . The value of F for equilibrium is x < < H
A hollow metallic sphere with internal and external radii r 1 and r 2 respectively floats on the surface of liquid. The density of liquid is ρ 1 and density of material of sphere is ρ 2 . What fraction of the sphere is inside the liquid?
A piece of ice floats in a vessel with water above which a layer of lighter oil is poured. When the whole of ice melts,which one of the following statements will be true?
An object when placed in water floats with one-third of its volume outside water. If it is placed in a liquid ‘X’, it floats with 3 4 of its volume outside the liquid. Density of the liquid ‘X’ is:
A body is floating in a liquid contained in a vessel.The whole system is falling under gravity.Upthrust on the body due to liquid is :
A cubical block of wood of specific gravity 0.5 and a chunk of concrete of specific gravity 2.5 are fastened together. The ratio of mass of wood to the mass of concrete which makes the combination to float with its entire volume submerged in water is:
In case of motion of fluid in a tube where area of cross section is minimum: (i) velocity is maximum (ii) velocity is minimum (iii) pressure is maximum (iv) pressure is minimum
The velocity of efflux of an ideal liquid does not depend on: (i) the depth of point below the free surface of liquid (ii) the area of orifice (iii) the density of liquid (iv) the area of cross-section of the vessel
A hole is in the bottom of the tank having water. If total pressure at the bottom is 3 atm (1 atm·= 105 Nm -2 ), then velocity of water flowing from hole is:
The cylindrical tube of a spray pump has a cross-section of 8cm 2 , one end of which has 40 fine holes each of area 10 – 8 m 2 . If the liquid flows inside the tube with a speed of 0.15 m-rnin -1 , the speed with which the liquid is ejected through the holes is :
A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m 2 • Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be : [ ρ air = 12 kg/m 3 ]
The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is:
Fire is caught at height of 125m from the fire brigade. To extinguish the fire, water is coming out from the pipe of cross-section 6.4cm with rate 950 litre/min. Find out minimum velocity of water exiting from fire brigade tank (g = 10 m/s 2 )
The total area of wings of an aeroplane is 10 m 2 .The speed of air above and below the wing is 140 m/s and 110 m/s. Then the force on the aeroplane by air is :
Consider the following statements (A) Specific gravity of a fluid is a dimensionless quantity. (B) It is the ratio of density of fluid to the density of water. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) An ice cube is floating in water in a vessel at 0 °C. When ice cube melts, level of water in the vessel remain same. (B) Volume of melted ice is same as volume of water displaced by ice. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) The apparent weight of a block of wood floating in water is equal to zero. (B) The value of acceleration due to gravity (g) in water becomes zero. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) A man sitting in a boat which is floating on a pond. If the man drinks some water from the pond, the level of water in the pond decreases. (B) In floating, the weight displaced by body is less than the weight of the body. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) A gas filled balloon stops rising after it has attained a certain height in the sky. (B) At the highest point in the sky, the density of air is such that the buoyant force on the balloon just equal its weight. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) Aeroplanes are made to run on the runway before take off, so that they acquire the necessary lift. (B) This is as per Bernoulli’s theorem, as velocity increases, pressure decreases and vice-versa . Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) To float, a body must displace liquid whose weight is greater than actual weight of the body. (B) In floating, the body will experience net downward force Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) The stream of water emerging from a water tap “necks down” as it falls. (B) The volume flow rate at different levels is same. Select the correct option.
Consider the following statements (A) Sudden fall of pressure at a place indicates storm. (B) Air flows higher pressure to lower pressure. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) The shape of an automobile is so designed that its front resembles the stream line pattern of the fluid through which it moves. (B) The shape of the automobile is made stream lined in order to reduce resistance offered by the fluid.
Consider the following statements (A) The rate of flow of a liquid through a capillary becomes non-linear when the pressure across capillary is increased. (B) With increase of pressure, the bore of capillary increases. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) The velocity increases, when water flowing in broader pipe enter a narrow pipe. (B) According to equation of continuity, product of area and velocity is constant. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) A wooden block with a coin placed on its top, floats in water as shown in figure. After some time the coin falls into the water, then both I and h decrease. (B) When coin falls into the water, block moves up and coin will displace less water in this situation. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) Soil particles inside water are freely placed but they stick together when taken out of water. (B) Thin films formed create pressure difference. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Consider the following statements (A) In an accelerated container pressure at A and B are same due to liquid column. (B) Gauge pressure is always directly proportional to depth of the liquid from surface. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
The coefficient of viscosity of a liquid can be defined from the equation F = ηA ( dv / dx ) where F is the tangential force between two liquid layers of area A. The layers are at a distance dy apart and du is the difference in their velocities. Suitable unit for dv/dx is:
The viscous force on a small sphere of radius R moving in a fluid varies as :
The terminal velocity of a small sized spherical body of radius r falling vertically in a viscous liquid is given by the following proportionality :
Terminal velocity of water drops depends upon the:
A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the Fig. drawn by:
Turbulent flow occurs when the Reynolds number is above:
X and Y are two capillary tubes with lengths l x and l y and with radii r x and r y respectively. When a pressure difference P is maintained between the ends of X, the rate of flow of water through X is 10 cc/sec. X and Y are now connected in series and the same pressure difference P is maintained across the combination. If l x = 2 l y and r x = r y , rate of flow of water through the combination will be:
If the terminal speed of a sphere of gold (density= 19.5 gm/cc) is 0.2 m/s in a viscous liquid (density= 1.5 gm/cc), find the terminal speed of a sphere of silver ( density = 10.5 gm/cc) of the same size in the same liquid.
Water is flowing with velocity 4 m/s in a cylinder of diameter 8 cm. It is connected to a pipe with its end tip of diameter 2 cm. The velocity of water at this free end is
A non-viscous fluid of constant density of 1000 kg/m 3 flows in a stream line motion along a tube of variable cross-section. The area of cross-section at two points P and Q of length 5m are 40cm 2 and 20cm 2 respectively. If velocity of fluid at P is 3 m/s then find velocity of fluid at Q.
Water is poured in a vessel at a constant rate β m 3 / s . . There is a small hole of area α at the bottom of the vessel. The maximum level of water in the vessel is proportional to :
Consider the following statements (A) Under steady flow the velocity of the particle of fluid is not constant at a point (B) Ideal fluids are compressible. Select the correct option. (a) (A) is false but (B) is true. (b) Both (A) and (B) are true. (c ) (A) is true but (B) is false. (d) Both (A) and (B) are false.
Sixty four spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5-ms -1 .If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is:
A sphere of radius R is gently dropped in a liquid of viscosity Tl in a vertical uniform tube. It attains a terminal velocity v. Another sphere of radius 2R when dropped into the same liquid will attain a terminal velocity:
Spherical balls of radius R are falling in a viscous fluid of viscosity Tl with a velocity v. The retarding viscous force acting on the spherical bali is:
A sphere of radius r and density p is dropped under gravity through a fluid of viscosity η . If the average acceleration is half of initial acceleration, what is the time required to attain terminal velocity? (Neglect buoyant force)
Two spheres of equal masses but radii r 1 and r 2 are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities are:
Viscous force is somewhat like friction as it opposes the motion and is non-conservative but not exactly so, because: (i) its velocity dependent while friction not (ii) its velocity independent while friction is (iii) its temperature dependent while friction not (iv) its independent of area like surface tension while friction depends
The volume of a liquid of density ρ and viscosity η flowing in time t through a capillary tube of length / and radius R, with a pressure difference P, across its ends is proportional to.
When there is no external force, the shape of a small liquid drop is determined by:
The surface tension of a liquid:
The surface tension of a liquid is 5 N/m. If a film is held on a ring of area 0.02 m 2 , its total surface energy is about:
The amount of work done in increasing the size of a soap film 10 x 6 cm to 10 x 10 cm is : (S.T. = 30 x 10 -3 N/m)
A spherical soap bubble has a radius r. The surface tension of the soap film is T. The energy needed to double the diameter of the bubble at the same temperature is:
The surface tension of a liquid is 70 dyne/cm. It may be expressed in M.K.S. system as:
The energy needed in breaking a drop of radius R into n drops of radius r is:
A soap bubble (surface tension 30 dyne/cm) has a radius of 2 cm. The work done in doubling its radius is:
A spherical liquid drop of radius R is divided into eight equal droplets: If surface tension is T, then work done in the process will .be:
A soap bubble assumes a spherical surface. Which of the given statements is wrong?
An air bubble of radius r in water is at a depth h below the water surface at some instant. If P is atmospfieric-pressure and d and T are the density and surface tension of water respectively, the pressure inside the bubble will be:
Two capillary tubes of different diameters are dipped in water. The rise of water is:
A capillary tube of radius r can support liquid of weight 6.28 x 10 -4 N. If the surface tension of the liquid is 5 x 10 -2 N/m, the radius of the capillary must be:
A capillary is dipped vertically in a liquid. The level in the capillary will be same as outside the capillary if the angle of contact is:
Water from inside the earth rises through the trunk of a big tree to leaves high up. The main reason for this is:
The mass of water that rises in capillary tube of radius R is M. The mass of water that rises in tube of radius 2R is:
Consider a liquid contained in a vessel. The liquid-solid adhesive force is very weak as compared to the cohesive force in the liquid. The shape of the liquid surface near the solid shall be:
Two soap bubbles of different radii are in communication with each other:
If two soap bubbles of radius r 1 and r 2 (> r1 ) are in contact, the radius of their common interface is:
A frame made of metallic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metallic wire is reduced by 50%, the energy of the soap film will be changed by:
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be :
The radius R of the soap , bubble is doubled under isothermal condition. If T be the surface tension of soap bubble, the required surface energy ln doing so is given by :
If for a liquid in a vessel force of cohesion is twice of adhesion: (i) the meniscus will be convex (ii) the liquid will wet the solid (iii) the angle of contact will be obtuse (iv) there will be capillary descent
A capillary tube is taken from the earth to the surface of moon. Rise of the liquid column on the moon (acceleration due to gravity on earth is 6 times that on moon) is:
A certain number of spherical drops of a liquid of radius ‘f coalesce to form a single drop of radius ‘R’ and volume ‘V’. If ‘T’ is the surface tension of the liquid, then :
A rectangular film of liquid is extended from ( 4cm x 2 cm) to (5 cm X 4 cm). If the work done is 3 X 10 -4 J, the value of the surface tension of the liquid is :
Find the maximum weight of needle which can float on water having surface tension 0.073 N/m if length of needle is 4 cm.
A liquid drop at temperature T, isolated from its surroundings, breaks into a number of droplets. The temperature of the droplets will be:
Consider the following statements. (A) For Reynolds number R e > 2000, the flow of fluid is turbulent. (B) Inertial forces are dominant compared to the viscous forces at such high Reynolds number. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Machine parts are jammed in winter. (B) The viscosity of lubricant used in machine parts increases at low temperature. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Hot soup tastes better than the cold soup, (B) Hot soup spread properly on our tongue due to lower surface tension. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) In gravity free space, the liquid in a capillary tube will rise to infinite height. (B) In the absence of gravity, there will be no force to prevent the rise of liquid due to surface te
Consider the following statements. (A) The shape of a liquid drop is spherical. (B) The pressure inside the drop is greater than that of outside. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) The small soap bubbles are spherical while large soap bubbles are flat ( oval) in shape (B) The surface tension of soap bubble decreases with size of bubble. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Water wets glass capillary while mercury does not wet. (B) The density of mercury is higher than glass while that of water is lower than glass Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) The tip of the nib of ink-pen is split. (B) The split in nib acts as the capillary. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) A conical pipe shown in Fig. has a drop of water. The water drop tends to move towards tapered end. (B) Excess pressure is directed towards centre of curvature and inversely proportional to radius of curvature. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Gases also behave as fluids. (B) Gas molecules are bonded by cohesive forces.
Consider the following statements. (A) On increase of temperature, surface tension decreases. (B) Interatomic separation increases on heating. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
With increase in temperature the viscosity of:
Two capillary tubes of same length l but radii r 1 and r 2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the radius r of the single tube, that can replace the two tubes, so that the rate of flow is same as before?
A small steel ball falls through water more slowly than through air primarily because of:
A small spherical solid ball is dropped from a height in a viscous liquid. Its journey in the liquid is best described in the Fig.
A small wooden ball, an oil drop and an air bubble each of radius r are moving up in a liquid of viscosity η . The terminal velocities of these three, i.e., v w , v o and v a respectively will be such that:
A sphere of mass M and radius R is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to :
Two capillaries of lengths L and 2L and of radii R and 2R are connected in series. The net rate of flow of fluid through them will be: (given rate of the flow through single capillary X = πPR 4 / 8 ηL ) )
A metal plate of area 10 3 cm 2 rests on a layer of oil 6 mm thick. A tangential force of 10 -2 N is applied on it to move it with a constant velocity of 6 cms -1 .The coefficient of viscosity of the liquid is:
A spherical body of diameter Dis falling in viscous medium. Its terminal velocity is proportional to :
Two objects A and B of equal density and radius r A = 1 mm and r B = 2 mm are moving in same medium then find the V ratio of their terminal velocity v B v A in the medium
Free surface of a liquid has a tendency to contract and minimise its surface area. This tendency is due to:
Small liquid drops assume spherical shape because:
When kerosene is sprinkled on the surface of a pond mosquitoes can no longer remain sitting over it because:
Find the difference of air pressure between the inside and outside of a soap bubble 5 mm in diameter if surface tension is 1.6 N/m.
Consider the following statements. (A) The angle of contact of a liquid decreases with increase in temperature. (B) With increase in temperature, the surface tension of liquid increases. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) A thin stainless steel needle can lay floating on a still water surface. (B) Any object floats when the buoyancy force balances the weight of the object. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) When height of a tube is less than liquid rise in the capillary tube, the liquid does not overflow. (B) Product of radius of meniscus and height of liquid in capillary tube is always remains constant. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) The shape of a small liquid drop is spherical. (B) Due to surface tension, liquid tends to occupy minimum surface area and for given volume, a sphere has minimum area. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
Consider the following statements. (A) Water ascends while mercury descends in a capillary tube. (B) Surface tension of water is positive while that of mercury is negative. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.
There will be no phenomenon of capillarity if
The flow of a fluid in a tube, laminar or turbulent, is determined by (a) The velocity of the fluid (b) Radius of the tube (c) The density of the fluid (d) The coefficient of viscosity of the fluid
A bottle is kept on the ground as shown in the figure. The bottle can be modelled as having two cylindrical zones. The lower zone of the bottle has a cross-sectional radius of R 2 and is filled with honey of density 2. The upper zone of the bottle is filled with the water of density ρ and has a cross-sectional radius R. The height of the lower zone is H while that of the upper zone is 2H. Now the honey and the water parts are mixed together to form a homogenous solution (Assume that total volume does not change). Column-I Column-II i. Net force on bottle in horizontal direction p. zero ii. Pressure at base of bottle before mixing of water and honey q. 9 2 ρgH iii. Preesure at the base after mixing r. 4 ρgH iv. Pressure at point P (figure) after making s. 3 ρgH Now match the given columns and select the correct option from the codes given below.
A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is burning at the rate of 2 cm/hour then the top of the candle will
Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = l0 m / s 2 )
A wooden block, with a coin placed on its top, floats in water as shown in fig. the distance l and h are shown there. After some time the coin falls into the water. Then
A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerine (density = l.3 g/ cm 3 ) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/ cm 3 is poured into the other arm until the upper surfaces of the oil and glycerine are in the same horizontal level. Find the length of the oil column, (Density of mercury = 13.6 g/ cm 3 ).
A cubical block of wood 10 cm on a side floats at the interface between oil and water, as in Fig. with its lower face 2 cm below the interface. The density of the oil is 0.6 g cm – 3 . The gauge pressure at the lower face of the block is
Two syringes of different cross section (without needle) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are I cm and 3 cm respectively. If the smaller piston is pushed in through 6 cm, how much does the longer piston move out?
ln figure, block A hangs by a cord from spring balance D and is submerged in a liquid C contained in a beaker B. The mass of the beaker is 1 kg. The mass of the liquid is 1.5 kg. Balance D reads 7.5 kg. The volume of block is 0.003 m 3 . The mass per unit volume of the liquid is
For the area a of the hole is much lesser than the area of the base of a vessel of liquid, velocity of effiux v of the liquid in an accelerating vessel is:
The speed of flow past the lower surface of a wing of an aeroplane is 50 ms – 1 . What speed of flow over the upper surface will-give a dynamic lift of 1000 Pa? Density of air = 1.3 kg m 3 .
Figure shows an ideal fluid flowing through a uniform cross-sectional tube. In the vertical tube with liquid velocities v A and v B and pressure P A and P B . Knowing that tube offers no resistance to fluid flow then which of the following is true.
An L-shaped tube with a small orifice is held in a water stream as shown in fig. The upper end of the tube is 10.6 cm above the surface of water. What will be the height of the jet of water coming from the orifice? (Velocity of water stream is 2.45 m/s)
Water is flowing in streamline motion in the tube shown in Fig. Pressure is
A cart supports a cubic tank filled with a liquid up to the top. The cart moves with a constant acceleration a in the horizontal direction. The tank is tightly closed. Assume that the lid does not exert any pressure on the liquid when in motion with uniform acceleration. The pressure at a point at a depth h and distance / from the front wall is:
An empty glass jar is submerged in tank of water with open mouth of the jar downwards, so that air inside the jar is trapped and cannot get out. As the jar is pushed down slowly, the magnitude of net buoyant force on the system of volume of gas trapped in the jar and the jar
A vessel with water is placed on a weighing pan and reads 600 g. Now a ball of 40 g and density 0.80 g/cc is sunk into the water with a pin as shown in fig. keeping it sunk. The weighing pan will show a reading
A tank with base area L 2 is filled with a liquid to height H. The tank is accelerated horizontally with acceleration a as shown in figure. If a small hole is made at the point A, then it is observed that the liquid does not come out of the tank. The magnitude of acceleration should be
A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration a towards right. Pressure is (i) maximum at, and (ii) minimum at
Water flows into a large tank with flat bottom at the rate of 10 − 4 m 3 / s . Water is also leaking out of a hole of area 1 cm 2 at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is : take g = 9.8 m / s 2
At room temperature a small sphere is falling through a viscous liquid at constant velocity of 10 cm/sec. If the temperature of liquid is increased by 30 o C, the terminal velocity of the sphere
The excess pressure in a soap bubble of radius 2 mm is Δp . What will be the radius of a soap bubble whose excess pressure is 2 Δp / 3 ?
Weight of an empty balloon is W 1 . Air of weight W is filled in the balloon and weight of the air filled balloon is W 2 . If the air inside the balloon has the same density as the outside air, then
If T is the surface tension of soap solution, the amount of work done is blowing a soap bubble from a diameter D to a diameter 2D is
A mercury drop of radius I cm is broken into 10 6 droplets of equal size. The work done is ( T = 35 × 10 – 2 N/m)
The radius of a soap bubble is increased from 1 π cm to 2 π cm. If the surface tension of water is 30 dynes per cm, then the work done will be
The surface tension of soap solution is 25 × 10 – 3 Nm – 1 . The excess pressure inside a soap bubble of diameter 1 cm is
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2 . 5 × 10 – 2 N/m. The pressure inside the bubble equals at a point Z 0 below the free surface of water in a container. Taking g = 10 m / s 2 , density of water = 10 3 kg / m 3 , the value of Z 0 is
A rectangular film of liquid is extended from (4 cm x 2 cm) to (5 cm x 4 cm). If the work done is 3 × 10 – 4 J , the value of the surface tension of the liquid is
Statement I: A needle placed carefully on the surface of water may float, whereas a ball of the same material will always sink. Statement II: The buoyancy of an object depends both on the material and shape of the object.
Two uniform solid balls of same density and of radii r and 2r are dropped in air and fall vertically downwards. The terminal velocity of the ball with radius r is 1 cm s – 1 , then the terminal velocity of the ball of radius 2r will be (neglect buoyant force on the balls.)
A container filled with viscous liquid is moving vertically downwards with constant speed 3 v 0 . At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed v 0 . The coefficient of viscosity is η . There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is
A uniform solid sphere of relative density 5 is released in water filled in a long vertical tube. Its terminal velocity achieved is V. If another uniform solid sphere of same material but double the radius is released in the same water then the terminal velocity achieved will be.
When a ball is released from rest in a very long column of viscous liquid, its downward acceleration is ‘a’ (just after release). Then its acceleration when it has acquired two third of the maximum velocity:
A cubical block of side ‘a’ and density ‘ ρ ‘ slides over a fixed inclined plane with constant velocity ‘v’. There is a thin film of viscous fluid of thickness ‘t’ between the plane and the block . Then the coefficient of viscosity of the thin film will be: (Acceleration due to gravity is g)
A ball is thrown vertically upwards at time t = 0. Air resistance is not negligible and the acceleration of free fall is g. The ball reaches a maximum height at time t = T and then descends, reaching terminal speed. Which graph best shows the variation with time t of the acceleration a of the ball
A rectangular metal plate has dimensions of 10 cm x 20 cm. A thin film of oil separates the plate from a fixed horizontal surface. The separation between the rectangular plate and the horizontal surface is 0.2 mm. An ideal string is attached to the plate and passes over an ideal pulley to a mass m. When m = 125 gm, the metal plate moves at constant speed of 5 cm/s across the horizontal surface. Then the coefficient of viscosity of oil in dyne-s/ cm 2 is (Use g = 1000 cm/ s 2 )
A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).
The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like
A metallic sphere of radius 1 . 0 × 10 – 3 m and density 1 . 0 × 10 4 kg / m 3 enters a tank of water, after a free fall through a distance of h in the earth’s gravitational field. If its velocity remains unchanged after entering water, determine the value of h. Given: coefficient of viscosity of water = 1 . 0 × 10 – 3 N – s / m 2 , g = 10 m / s 2 and density of water: 1 . 0 × 10 3 kg / m 3 .
A drop of water of radius 0.0015 mm is falling in air. If the coefficient of viscosity of air is 1 . 8 × 10 – 5 kg / ( m – s ) , what will be the terminal velocity of the drop? (density of water = 1 . 0 × 10 3 kg / m 2 and g = 9 . 8 m / s 2 ) Density of air can be neglected.
Coefficient of viscosity of water =0.01 poise, density of water = 1 g cm – 3 . Then the maximum velocity with which water can flow through a capillary tube of radius 0.05 cm, without turbulent flow setting in, is
A metal ball B 1 (density 3.2 g/cc) is dropped in water, while another metal ball B 2 (density 6.0 g/cc) is dropped in a liquid of density 1.6 g/cc.If both the balls have the same diameter and attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is
The terminal velocity of a 2 cm radius ball in a viscous liquid is 20 cm s – 1 . What would be the terminal velocity if the radius of the ball were halved?
A small steel ball falls through a syrup at a constant speed of 10 cm s – 1 . If the steel ball is pulled upwards with a force equal to twice its effective weight, how fast will it move upward?
A small steel ball of mass m and radius r is falling under gravity through a viscous liquid of coefficient of viscosity η . lf g is the value of acceleration due to gravity, then the terminal velocity of the ball is proportional to (ignore buoyancy)
A copper ball of radius r is moving with a uniform velocity u in the mustard oil. The dragging force acting on the ball is F. The dragging force on the copper ball of radius 2r moving with uniform velocity 2u in the mustard oil is
A force of 3.14 N is required to drag a sphere of radius 4 cm with a speed of 5 m/s in a medium in gravity free space. The coefficient of viscosity of the medium is
A rain drop of radius 0.3 mm falling vertically downwards in air has a terminal velocity of 1 m/s. The viscosity of air is 18 x 10 – 5 poise. The viscous force on the drop is
A space 2.5 cm wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area 0.5 m 2 just midway the surfaces at a speed of 0.5 m/sec is 1 N. The coefficient of viscosity in kg – s/ m 2 is:
Find the minimum force required to drag a hard polythene plate of area 2 m 2 on a thin film of oil of thickness 0.25 cm and η = 15 poise. Assume the speed of the plate is 10 cm/s.
A metal plate of area 2 m 2 is pulled horizontally with a velocity of 0.5 ms – 1 on a liquid layer 1 mm thick. The force required, if the viscosity of liquid is 12 N s m – 2 is
Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 75 x 10 – 4 newton force due to the weight of the liquid. If the surface tension of water is 6 × 10 – 2 newton/metre the inner circumference of the capillary must be:
Water rises to a height of 2 cm in a capillary tube. If the tube is tilted 60° from the vertical, water will rise in the tube to a length
Assuming the xylem tissues through which water rises from root to the branches in a tree to be of uniform cross section find the maximum radius of xylem tube in a 10 m high coconut tree so that water can rise to the top. (surface tension of water = 0.1 N/m, Angle of contact of water with xylem tube = 60°)
A capillary of the shape as shown is dipped in a liquid. Contact angle between the liquid and the capillary is 0° and effect of liquid inside the meniscus is to be neglected. T is surface tension of the liquid, r is radius of the meniscus, g is acceleration due to gravity and ρ is density of the liquid then height h in equilibrium is:
The correct curve between the height or depression h of liquid in a capillary tube and its radius is
The pressure inside a small air bubble of radius 0.1 mm situated just below the surface of water will be equal to [Take surface tension of water 70 × 10 – 3 Nm – 1 and atmospheric pressure = 1 . 013 × 10 5 Nm – 2 ]
A soap bubble is blown with the help of a mechanical pump at the mouth of a tube. The pump produces a certain increase per minute in the volume of the bubble, irrespective of its internal pressure. The graph between the pressure inside the soap bubble and time t will be
A soap bubble of radius R is surrounded by another soap bubble of radius 2R, as shown. Take surface tension = S. Then, the pressure inside the smaller soap bubble, in excess of the atmospheric pressure, will be
Two mercury drops, each of radius r, merge to form a bigger drop. If σ is the surface tension of mercury then the surface energy released is
A spherical drop of water has 1 mm radius. If the surface tension of the water is 50 × 10 – 3 N/m, then the difference of pressure between inside and outside the spherical drop is:
What is the Buoyancy force acting on a body of mass 1 kg having volume of 1000 cm 3 when immersed in water in a Geostationary satellite when it is half immersed. (in newton)
A capillary tube of radius 0.20 mm is dipped vertically in water. The height of the water column raised in the tube, will be (surface tension of water = 0.075 N/m and density of water = 1000 kg/ m 3 . Take g = 10 m / s 2 and contact angle 0°).
Water rise in capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 × 10 – 3 N / m , then the diameter of capillary will be (Take angle of contact = 0°)
When a capillary tube is dipped in water, water rises upto 8 cm in the tube. What happens when the tube is pushed down such that its end is only 5 cm above outside water level?
Two spherical soap bubbles of radii r 1 and r 2 in vacuum coalesce under isothermal condition. The resulting bubble has a radius R such that
A capillary tube of radius r is immersed in a liquid. The liquid rises to a height h. The corresponding mass is m. What mass of water shall rise in the capillary if the radius of the tube is doubled?
The excess pressure due to surface tension inside a spherical drop is 6 units. If eight such drops combine, then the excess pressure due to surface tension inside the larger drop is
Water rises to a height of 10 cm in a glass capillary tube. If the area of cross-section of the tube is reduced to one fourth of the former value, what is the height of water rise now?
An open capillary tube is lowered in a vessel with mercury. The difference between the levels of the mercury in the vessel and in the capillary tube ∆ h = 4 . 6 mm . What is the radius of curvature of the mercury meniscus in the capillary tube? Surface tension of mercury is 0.46 N/m, density of mercury is 13.6 gm/cc.
A water film is made between two straight parallel wires of length 10 cm each and at a distance of 0.5 cm from each other. If the distance between the wires is increased by 1 mm, how much work will be done ? Surface tension of water = 72 dynes/cm.
An annular disc of radius r 1 = 10 cm and r 2 = 5 cm is placed on a water surface. Find the surface tension force on the disc if we want to pull it from water surface. Take surface tension σ = 7 × 10 – 3 N / m , g = 10 m / s 2
Calculate the energy spent in spraying a drop of mercury of r radius into N droplets all of same size. If the surface tension of mercury is T.
A soap bubble has radius r. The work done in increasing its radius to three times its original radius, without any rise of temperature, is (Given: surface tension of soap solution is T)
The surface tension of a liquid is 5 N m – 1 . If a thin film formed on a loop of area 0.02 m – 2 then its surface energy will be
If work W is done in blowing a bubble of radius R from a soap solution, then the work done in blowing a bubble of radius 2R from the same solution is
A soap film measure 10 cm x 6 cm. It is increased to 10 cm x 12 cm. If surface tension is 30 x 10 – 3 newton per metre, then the work done is
A square wire frame of length l is dipped in a solution. When the frame is taken out, a liquid film is formed. What is the algebraic sum of all the force acting on the frame due to surface tension of the liquid? (Given: σ = surface tension of the liquid).
Consider a vertical parallel of semi-circular cross-section dipped in a liquid. Assume that the wetting of the tube is complete. The force of surface tension on the flat part and on curved part of the tube are in the ratio
A wire ring of diameter 14 cm is gently lowered on to a liquid surface and then pulled up. When the film just breaks, the force required is 0.0616 N. The surface tension of the liquid is
A wire of mass 1 g is kept horizontally on the surface of water. The length of the wire that does not break the surface film is (surface tension of water is 70 dyne cm – 1 )
A disc of paper of radius R has a hole of radius r. It is floating on a liquid of surface tension T. The force of surface tension on the disc is
The surface tension of water is 75 dyne/cm. Find the minimum vertical force required to pull a thin wire ring up (refer figure) if it is initially resting on a horizontal water surface. The circumference of the ring is 20 cm and its weight is 0.1 N
A long capillary tube of mass ‘ π ‘ gm, radius 2 mm and negligible thickness, is partially immersed in a liquid of surface tension 0.1 N/m. Take angle of contact zero and neglect buoyant force of liquid. The force required to hold the tube vertically, will be ( g = 10 m / s 2 )
The figure shows a soap film in which a closed elastic thread is lying. The film inside the thread is pricked. Now the sliding wire is moved out so that the surface area increases. The radius of the circle formed by elastic thread will
A large number of water drops each of radius r combine to have a drop of radius R. If the surface tension is T and the mechanical equivalent of heat is J, then the rise in temperature will be
There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius R. If the surface tension of the loop be T, then what will be the tension in the thread?
A film of water is formed between two straight parallel wires of length 10 cm each separated by 0.5 cm. If their separation is increased by 1 mm while still maintaining their parallelism, how much work will have to be done (Surface tension of water = 7 .2 x 10 – 2 N/m)
One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy is
A thin liquid film formed between a U shaped wire and a light slider supports a weight of 1 . 5 × 10 – 2 N, as shown in the figure. The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is
A thin metal disc of radius r floats on water surface and bends the surface downwards along the perimeter making an angle θ with vertical edge of the disc. If the disc displaces a weight of water W and surface tension of water is T, then the weight of metal disc is
Energy needed in breaking a drop of radius R into n drops of radii r is given by
The maximum force, in addition to the weight required to pull a wire of 5.0 cm long from the surface of water at temperature 20°C, is 728 dynes. The surface tension of water is
A thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out. The frame is completely covered with the film. When the portion A punctured with a pin, the thread.
A log of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sink should be (density of wood = 600 kg/ m 3 )
When ice melts completely, level of liquid in which ice is submerged Column-i Coluumn-ii i. p. Increases ii. q. Decreases iii. r. Remains same iv. Density of oil is greater than density of ice Density of oil is less than densiry of water s. May increases or decreases Now match the given colurnns and select the correct option from the codes given below. Codes
A solid sphere of density η (> 1) times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m then the tension in the string is given by
A hemispherical bowl just floats without sinking in a liquid of density 1 . 2 × 10 3 kg / m 3 . If outer diameter and the density of the bowl are 1 m and 2 x 10 4 kg / m 3 respectively, then the inner diameter of the bowl will be
A Pitot tube is shown in figure. Wind blows in the direction shown. Air at inlet A is brought to rest, whereas its speed just outside of opening B is unchanged. The U tube contains mercury of density ρ m . Find the speed of wind with respect to Pitot tube. Neglect the height difference between A and B and take the density of air as ρ a .
A liquid flows through a horizontal tube as shown in figure. The velocities of the liquid in the two sections, which have areas of cross-section A 1 and A 2 are v 1 and v 2 , respectively. The difference in the levels of the liquid in the two vertical tubes is h.Then
Water from a tap emerges vertically downwards with an initial velocity V 0 . Assume pressure is constant throughout the stream of water and the flow is steady. Find the distance from the tap at which cross – sectional area of stream is half of the cross-sectional area of stream at the tap.
An ideal fluid is flowing through the given tubes which is placed on a horizontal surface. If the liquid has velocities V A and V B , and pressures P A and P B at points A and B respectively, then the correct relation is (A and B are at same height from ground level, the figure shown is as if the system is seen from the top):
A broad vessel, with a square base of edge a = 10 cm is separated into two halves A and B, by a smooth vertical piston. A spring of spring constant k = 1500 N/m is filled across the compartment A and the compartment B is filled with water to a height 20 cm. Find the compression in the spring.
A tube 1 cm 2 in cross-section is attached to the top of a vessel 1 cm high and of cross-section 100 cm 2 . Water is poured into the system filling it to a depth of 100 cm above the bottom of the vessel as shown in Fig. Take g = 10 ms – 2 . Now
An V shaped glass tube is kept inside a bus that is moving with constant acceleration. During the motion, the level of the liquid in the left arm is at 12 cm whereas in the right arm, it is at 8 cm when the orientation of the tube is as shown. Assuming that the diameter of the tube is much smaller than levels of the liquid and neglecting effect of surface tension, acceleration of the bus will be (g = 10 m / s 2 ).
Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right hand vessel (s = relative density of mercury and ρ = density of water) by
A tank with a square base of area 2 m 2 is divided into two compartments by a vertical partition in the middle. There is a small hinged door of face area 20 cm 2 at the bottom of the partition. Water is filled in one compartment and an acid of relative density 1.5 in the other, both to a height of 4 m. The force necessary to keep the door closed is (Take g = 10 ms – 2 )
In a vertical tube of variable cross section water is flowing as shown in figure. If p 1 and p 2 be respectively, then
A cylinder of cork is floating in water in a container closed at the top as shown in the figure. Now more air is introduced into the container so that pressure of air on the free surface is increased. Then volume of water displaced by the cork
A wooden cylinder is floating in water with its axis vertical and its submerged length is 10 cm. If it is slightly pushed into water and released, its starts oscillating with time period T. If g = 10 m/s 2 find T in second.
A fluid is flowing through a pipe of variable cross-sectional area. A and B are two points in the flowing fluid. We can write Bernoulli’s equation between two points A and B if
A slider PQ is kept on the parallel arms of a U-shaped wire frame as shown in figure. A soap film is formed in the space enclosed by the slider and U-shaped wire frame and the slider is held in position by an external agent. The film is horizontal. Now the slider is displaced to the right along the parallel arms and released. Then after release
A thin wire AOB is bent at point O and kept in a vertical position. A soap film is formed between a slider PRSQ and the bent wire. Initially the slider PRSQ is in equilibrium in the position shown. Now the slider is slightly pulled downward and released. Then after release
A small steel sphere is allowed to fall in a long vertical viscous liquid column. When the sphere has achieved 50% of its terminal velocity, its acceleration is [take g = 10 m/s 2 ; ignore buoyant force]
A liquid having viscosity η and density ρ is flowing through a pipe of diameter d and its critical velocity is found to be 0.8 m/s. Then critical velocity of another liquid having coefficient of viscosity η / 2 , density ρ / 2 flowing through a pipe of diameter d/2 will be
A cube having length of side 10 cm and made of a material of density 4 gm/cm 3 , is projected horizontally with a velocity of 4 m/s on a horizontal surface. There is a thin film off grease of thickness 0.2 mm between the cube and the horizontal surface. If the cube stops after travelling a distance of 10 m, the viscosity of grease in N-S/m 2 is
A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at its sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rps , the difference in the height of liquid at the centre of the vessel and its sides is
A car containing a beaker of water is moving horizontally on a level road. Consider two points, A & B, inside the water such that they are on the same horizontal level and are separated by a distance L. Which of the following options is correct regarding the pressure differences between those two points?
At what speed is the velocity head of water equal to pressure head of 40 cm of Hg ?
A plane is in level flight at constant speed and each of its two wings has an area of 25 m 2 . If the speed of the air on the upper and lower surfaces of the wing are 270 km / h and 234 km/h respectively, then what must have been the mass of the plane? (Take the density of the air = 1 kg m – 3 )
A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3. 10 atm. The stored gasoline has a density of 660 kgm – 3 . The velocity with which gasoline begins to shoot out of the hole is
A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m /s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise, distance between the plates in m is
An incompressible liquid travels as shown in the figure. The speed of the fluid in the lower branch will be
A small steel ball of radius r experiences a viscous force F when it is falling in a jar of glycerine with terminal velocity v. The viscons force experienced by a steel ball of radius r/2 falling in glycerine with terminal velocity v/2 is
A vertical capillary with inner diameter 0.50 mm is submerged into water so that the length of its part protruding over the water surface in 25 mm. The radius of curvature of the meniscus is x × 10 − 4 m . Find x to nearest integer. (Surface tension of water = 73 × 10 − 3 N / m ).
Two capillary tubes A and B of equal radii r a = r b = r and equal lengths l a = l b = l are held horizontally. When the same pressure difference P is maintained across each tube, the rate of flow of water in each is Q. If the tubes are connected in series and the same pressure difference P is maintained across the combination, the rate of flow through the combination will be
A block of wood floats in a liquid with four-fifths of its volume submerged. If the relative density of wood is 0.8, what is the the density of the liquid in units of kg m -3 ?
If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake
Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g / cm 3 . If the mass of the other is 48 g, its density in g / cm 3 is
An inverted bell lying at the bottom of a lake 47.6 m deep has 50 cm 3 of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm 3 )
Equal masses of water and a liquid of density 2 are mixed together, then the mixture has a density of
The pressure at the bottom of a tank containing a liquid does not depend on
A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating up the reading will be
The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to
A barometer tube reads 76 cm of mercury. If the tube is gradually inclined at an angle of 60 o with vertical, keeping the open end immersed in the mercury reservoir, the length of the mercury column will be
A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/cm 3 ) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/cm 3 is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm 3
If two liquids of same masses but densities ρ 1 and ρ 2 respectively are mixed, then density of mixture is given by
A triangular lamina of area A and height h is immersed in a liquid of density ρ in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is
Three liquids of densities d,2d and 3d are mixed in equal proportions of weights. The relative density of the mixture is
From the adjacent figure, the correct observation is
Why the dam of water reservoir is thick at the bottom
A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity ω then
Air is blown through a hole on a closed pipe containing liquid. Then the pressure will
An ice berg of density 900 Kg/m 3 is floating in water of density 1000 Kg/m 3 . The percentage of volume of ice-cube outside the water is
Radius of an air bubble at the bottom of the lake is r and it becomes 2r when the air bubbles rises to the top surface of the lake. If P cm of water be the atmospheric pressure, then the depth of the lake is
A log of wood of mass 120 Kg floats in water. The weight that can be put on the raft to make it just sink, should be (density of wood = 600 Kg/m 3 )
A hemispherical bowl just floats without sinking in a liquid of density 1.2 × 10 3 kg/m 3 . If outer diameter and the density of the bowl are 1 m and 2 × 10 4 kg/m 3 respectively, then the inner diameter of the bowl will be
In making an alloy, a substance of specific gravity s 1 and mass m 1 is mixed with another substance of specific gravity s 2 and mass m 2 ; then the specific gravity of the alloy is
A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be
A metallic block of density 5 gm cm -3 and having dimensions 5 cm × 5 cm × 5 cm is weighed in water. Its apparent weight will be
A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g/3, the fraction of volume immersed in the liquid will be
A silver ingot weighing 2.1 kg is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of silver is 10.5. The tension in the string in kg-wt is
Two solids A and B float in water. It is observed that A floats with half its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B
The fraction of a floating object of volume V 0 and density d 0 above the surface of a liquid of density d will be
Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by
A block of steel of size 5 cm × 5 cm × 5 cm is weighed in water. If the relative density of steel is 7, its apparent weight is
A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body
A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring
A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water
A rectangular block is 5 cm × 5 cm × 10cm in size. The block is floating in water with 5 cm side vertical. If it floats with 10 cm side vertical, what change will occur in the level of water?
A solid sphere of density η ( > 1) times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m then the tension in the string is given by
A ball whose density is 0.4 × 10 3 kg/m 3 falls into water from a height of 9 cm . To what depth does the ball sink
Two solids A and B float in water. It is observed that A floats with 1 2 of its body immersed in water and B floats with 1 4 of its volume above the water level. The ratio of the density of A to that of B is
Two pieces of metal when immersed in a liquid have equal upthrust on them; then
A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water
A wooden cylinder floats vertically in water with half of its length immersed. The density of wood is
A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is burning at the rate of 2cm/hour then the top of the candle will
A large ship can float but a steel needle sinks because of
An ice block contains a glass ball when the ice melts within the water containing vessel, the level of water
Construction of submarines is based on
In which one of the following cases will the liquid flow in a pipe be most streamlined
Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is
Water enters through end A with speed v 1 and leaves through end B with speed v 2 of a cylindrical tube AB. The tube is always completely filled with water. In case I tube is horizontal and in case II it is vertical with end A upwards and in case III it is vertical with end B upwards. We have v 1 = v 2 for
The velocity of kerosene oil in a horizontal pipe is 5 m/s. If g = 10 m / s 2 then the velocity head of oil will be
An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is
Water is moving with a speed of 5.18 ms -1 through a pipe with a cross-sectional area of 4.20 cm 2 . The water gradually descends 9.66 m as the pipe increase in area to 7.60 cm 2 . The speed of flow at the lower level is
In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the
Air is streaming past a horizontal air plane wing such that its speed in 120 m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg per metre 3 and the wing is 10 m long and has an average width of 2 m , then the difference of the pressure on the two sides of the wing of
A manometer connected to a closed tap reads 3.5 × 10 5 N/m 2 . When the valve is opened, the reading of manometer falls to 3.0 × 10 5 N/m 2 , then velocity of flow of water is
A large tank filled with water to a height ‘h’ is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h 2 and from h 2 to zero is
A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s ) through a small hole on the side wall of the cylinder near its bottom is
There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm (1 atm = 10 5 N/m 2 ) then the velocity of water flowing from hole is
There is a hole of area A at the bottom of cylindrical vessel. Water is filled up to a height h and water flows out in t second. If water is filled to a height 4h, it will flow out in time equal to
A cylindrical tank has a hole of 1 cm 2 in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 70 cm 3 /sec. then the maximum height up to which water can rise in the tank is
A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.001 poise, distance between the plates in m is
Spherical balls of radius ‘r’ are falling in a viscous fluid of viscosity ‘ η ‘ with a velocity ‘v’. The retarding viscous force acting on the spherical ball is
A small sphere of mass m is dropped from a great height. After it has fallen 100 m, it has attained its terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first 100 m of fall is
A ball of radius r and density ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is η , the value of h is given by
Two drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be
A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference P. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is
The rate of steady volume flow of water through a capillary tube of length ‘l’ and radius ‘r’ under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)
We have two (narrow) capillary tubes T 1 and T 2 . Their lengths are l 1 and l 2 and radii of cross-section are r 1 and r 2 respectively. The rate of flow of water under a pressure difference P through tube T 1 is 8cm 3 /sec. If l 1 = 2l 2 and r 1 =r 2 , what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before (= P)
In a turbulent flow, the velocity of the liquid molecules in contact with the walls of the tube is
In a laminar flow the velocity of the liquid in contact with the walls of the tube is
The Reynolds number of a flow is the ratio of
Water is flowing through a tube of non-uniform cross-section ratio of the radius at entry and exit end of the pipe is 3 : 2. Then the ratio of velocities at entry and exit of liquid is
Water is flowing through a horizontal pipe of non-uniform cross-section. At the extreme narrow portion of the pipe, the water will have
A liquid flows in a tube from left to right as shown in figure. A 1 and A 2 are the cross-sections of the portions of the tube as shown. Then the ratio of speeds v 1 / v 2 will be
An application of Bernoulli’s equation for fluid flow is found in
The Working of an atomizer depends upon
The pans of a physical balance are in equilibrium. Air is blown under the right hand pan; then the right hand pan will
In a streamline flow
At what speed the velocity head of a stream of water be equal to 40 cm of Hg
The weight of an aeroplane flying in air is balanced by
A tank is filled with water up to a height H. Water is allowed to come out of a hole P in one of the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D
A cylindrical vessel of 90 cm height is kept filled upto the brim. It has four holes 1, 2, 3, 4 which are respectively at heights of 20 cm, 30 cm, 45 cm and 50 cm from the horizontal floor PQ. The water falling at the maximum horizontal distance from the vessel comes from
A rectangular vessel when full of water takes 10 minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water
A good lubricant should have
We have three beakers A, B and C containing glycerine, water and kerosene respectively. They are stirred vigorously and placed on a table. The liquid which comes to rest at the earliest is
The rate of flow of liquid in a tube of radius r, length l, whose ends are maintained at a pressure difference P is V = πQP r 4 ηl where η is coefficient of the viscosity and Q is
In Poiseuilli’s method of determination of coefficient of viscosity, the physical quantity that requires greater accuracy in measurement is
Two capillary tubes of the same length but different radii r 1 and r 2 are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before
Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes
Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a tube of diameter 2 cm. The velocity of water in the other pipe is
What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are ρ and σ respectively, and the viscosity of the liquid is η ).
Consider the following equation of Bernouilli’s theorem. P + 1 2 ρV 2 + ρgh = K (constant). The dimensions of K/P are same as that of which of the following
A homogeneous solid cylinder of length L ( L < H / 2 ) . Cross-sectional area A / 5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L / 4 in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure P 0 . Then density D of solid is given by
A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is
Water is filled in a cylindrical container to a height of 3m. The ratio of the cross-sectional area of the orifice and the beaker is 0.1. The square of the speed of the liquid coming out from the orifice is (g = 10 m/s 2 )
A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water the quantities of water flowing out per second from both the holes are the same. Then R is equal to
A cylinder containing water up to a height of 25 cm has a hole of cross-section 1 4 cm 2 in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density ρ . The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is
A uniform rod of density ρ is placed in a wide tank containing a liquid of density ρ 0 ( ρ 0 > ρ ) . The depth of liquid in the tank is half the length of the rod. The rod is in equilibrium, with its lower end resting on the bottom of the tank. In this position the rod makes an angle θ with the horizontal
A block of ice floats on a liquid of density 1.2 in a beaker then level of liquid when ice completely melt
A lead shot of 1mm diameter falls through a long column of glycerine. The variation of its velocity v. with distance covered is represented by
Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure p at points along the axis is represented by
A small spherical solid ball is dropped from a great height in a viscous liquid. Its journey in the liquid is best described in the diagram given below by the
A vessel of area of cross-section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from H 1 to H 2 will be
The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed v with which the liquid is crossing points at a distance X from O along a radius XO would look like
The radius of a spherical soap bubble is r and surface tension of soap water is T respectively. Find the charge uniformly distributed over the outer surface of the bubble is required to double its radius. (Atmospheric pressure is P o and inside temperature of the bubble during expansion remain constant)
The spherical shape of rain-drop is due to
The temperature at which the surface tension of water is zero
A small air bubble is at the inner surface of the bottom of a beaker filled with cold water. Now water of the beaker is heated. The size of bubble increases. The reason for this may be
Small droplets of a liquid are usually more spherical in shape than larger drops of the same liquid because
Which of the fact is not due to surface tension
Water does not wet an oily glass because
A water drop takes the shape of a sphere in a oil while the oil drop spreads in water, because
In the glass capillary tube, the shape of the surface of the liquid depends upon
Hairs of shaving brush cling together when it is removed from water due to
Force necessary to pull a circular plate of 5 cm radius from water surface for which surface tension is 75 dynes/cm, is
The property of surface tension is obtained in
The surface tension of a liquid
If two glass plates are quite nearer to each other in water, then there will be force of
Consider a liquid contained in a vessel. The liquid solid adhesive force is very weak as compared to the cohesive force in the liquid. The shape of the liquid surface near the solid shall be
Two pieces of glass plate one upon the other with a little water in between them cannot be separated easily because of
A 10 cm long wire is placed horizontally on the surface of water and is gently pulled up with a force of 2 ×10 -2 N to keep the wire in equilibrium. The surface tension, in Nm -1 , of water is
It is easy to wash clothes in hot water because its
Due to which property of water, tiny particles of camphor dance on the surface of water
A wooden stick 2m long is floating on the surface of water. The surface tension of water 0.07 N/m. By putting soap solution on one side of the sticks the surface tension is reduced to 0.06 N/m. The net force on the stick will be
A thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out. The frame is completely covered with the film. When the portion A punctured with a pin, the thread.
Surface tension may be defined as
Energy needed in breaking a drop of radius R into n drops of radii r is given by
The potential energy of a molecule on the surface of liquid compared to one inside the liquid is
A drop of liquid of diameter 2.8 mm breaks up into 125 identical drops. The change in energy is nearly (S.T. of liquid =75 dynes/cm)
Work done in splitting a drop of water of 1 mm radius into 10 6 droplets is (Surface tension of water = 72 × 10 − 3 J / m 2 )
The amount of work done in blowing a soap bubble such that its diameter increases from d to D is (T= surface tension of the solution)
A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension is T, then the work done in this process will be
The radius of a soap bubble is increased from 1 π cm to 2 π cm. If the surface tension of water is 30 dynes per cm, then the work done will be
If work W is done in blowing a bubble of radius R from a soap solution, then the work done in blowing a bubble of radius 2R from the same solution is
If two identical mercury drops are combined to form a single drop, then its temperature will
A spherical drop of oil of radius 1 cm is broken into 1000 droplets of equal radii. If the surface tension of oil is 50 dynes/cm, the work done is
If the surface tension of a liquid is T, the gain in surface energy for an increase in liquid surface by A is
A mercury drop of 1 cm radius is broken into 10 6 small drops. The energy used will be (surface tension of mercury is 35 × 10 − 3 N / cm )
The surface tension of liquid is 0.5 N/m. If a film is held on a ring of area 0.02 m 2 , its surface energy is
The amount of work done in forming a soap film of size 10 cm × 10 cm is (Surface tension T = 3 × 10 − 2 N / m )
What is ratio of surface energy of 1 small drop and 1 large drop, if 1000 small drops combined to form 1 large drop
When 10 6 small drops coalesce to make a new larger drop then the drop’s
8 mercury drops coalesce to form one mercury drop, the energy changes by a factor of
When two small bubbles join to form a bigger one, energy is
A film of water is formed between two straight parallel wires of length 10cm each separated by 0.5 cm. If their separation is increased by 1 mm while still maintaining their parallelism, how much work will have to be done (Surface tension of water = 7 .2 × 10 − 2 N / m )
Radius of a soap bubble is increased from R to 2R work done in this process in terms of surface tension is
The work done in blowing a soap bubble of radius 0.2 m is (the surface tension of soap solution being 0.06 N/m)
In order to float a ring of area 0.04 m 2 in a liquid of surface tension 75 N/m, the required surface energy will be
If two soap bubbles of equal radii r coalesce then the radius of curvature of interface between two bubbles will be
A liquid is coming out from a vertical tube. The relation between the weight of the drop W, surface tension of the liquid T and radius of the tube r is given by, if the angle of contact is zero
The angle of contact between glass and mercury is
The parts of motor cars are polished by chromium because the angle of contact between water and chromium is
A mercury drop does not spread on a glass plate because the angle of contact between glass and mercury is
A glass plate is partly dipped vertically in the mercury and the angle of contact is measured. If the plate is inclined, then the angle of contact will
The value of contact angle for kerosene with solid surface.
If a water drop is kept between two glass plates, then its shape is
A liquid wets a solid completely. The meniscus of the liquid in a sufficiently long tube is
If the surface of a liquid is plane, then the angle of contact of the liquid with the walls of container is
If two soap bubbles of different radii are in communication with each other
When two soap bubbles of radius r 1 and r 2 ( r 2 > r 1 ) coalesce, the radius of curvature of common surface is
The pressure of air in a soap bubble of 0.7cm diameter is 8 mm of water above the pressure outside. The surface tension of the soap solution is
The pressure at the bottom of a tank containing a liquid does not depend on
In capillary tube, pressure below the curved surface of water will be
Two soap bubbles of radii r 1 and r 2 equal to 4 cm and 5 cm are touching each other over a common surface S 1 S 2 (shown in figure). Its radius will be
The pressure inside a small air bubble of radius 0.1 mm situated just below the surface of water will be equal to [Take surface tension of water 70 × 10 − 3 Nm − 1 and atmospheric pressure = 1 .013 × 10 5 Nm − 2 ]
If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm, then the surface tension of soap solution will be (r = 1 cm and density d = 0.8 gm/cc)
In Jager’s method, at the time of bursting of the bubble
The excess pressure in a soap bubble is thrice that in other one. Then the ratio of their volume is
When two capillary tubes of different diameters are dipped vertically, the rise of the liquid is
Due to capillary action, a liquid will rise in a tube, if the angle of contact is
Two parallel glass plates are dipped partly in the liquid of density ‘d’ keeping them vertical. If the distance between the plates is ‘x’, surface tension for liquids is T and angle of contact is θ , then rise of liquid between the plates due to capillary will be
Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 75 × 10 − 4 N force due to the weight of the liquid. If the surface tension of water is 6 × 10 − 2 Nm − 1 , the inner circumference of the capillary must be
Two capillaries made of same material but of different radii are dipped in a liquid. The rise of liquid in one capillary is 2.2 cm and that in the other is 6.6 cm. The ratio of their radii is
Two capillaries made of the same material with radii r 1 = 1 mm and r 2 = 2 mm . The rise of the liquid in one capillary ( r 1 = mm ) is 30 cm, then the rise in the other will be
When a capillary is dipped in water, water rises to a height h. If the length of the capillary is made less than h, then
Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 × 10 -3 N/m, then the diameter of capillary will be
A capillary tube made of glass is dipped into mercury. Then
By inserting a capillary tube upto a depth l in water, the water rises to a height h. If the lower end of the capillary is closed inside water and the capillary is taken out and closed end opened, to what height the water will remain in the tube
If the surface tension of water is 0.06 Nm -1 , then the capillary rise in a tube of diameter 1 mm is ( θ =0° and g = 10 ms -2 )
If the diameter of a capillary tube is doubled, then the height of the liquid that will rise is
A capillary tube when immersed vertically in liquid records a rise of 3 cm. If the tube is immersed in the liquid at an angle of 60 o with the vertical. The length of the liquid column along the tube is
The liquid meniscus in capillary tube will be convex, if the angle of contact is
In the state of weightlessness, a capillary tube is dipped in water, then water
The correct relation is
During capillary rise of a liquid in a capillary tube, the surface of contact that remains constant is of
Water rises to a height h in a capillary at the surface of earth. On the surface of the moon the height of water column in the same capillary will be
Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 60 and 50 dyne/cm respectively Ratio of heights of liquids in the two tubes h 1 h 2 is
Two long capillary tubes A and B of radius R B > R A dipped in same liquid. Then
In a capillary tube experiment, a vertical 30 cm long capillary tube is dipped in water. The water rises up to a height of 10cm due to capillary action. If this experiment is conducted in a freely falling elevator, the length of the water column becomes
In a capillary tube, water rises to 3 mm. The height of water that will rise in another capillary tube having one-third radius of the first is
Water rises against gravity in a capillary tube when its one end is dipped into water because
A metallic sphere floats in an immiscible mixture of water ρ W = 10 3 kg / m 3 and a liquid ρ L = 13 ⋅ 5 × 10 3 kg / m 3 such that its 4/5th portion is in water and 1/5th portion in the liquid. The density of metal is
A sphere of radius R has a concentric cavity o{ radius r. The relative density of the material of the sphere is o. It just floats when placed in a tank full of water. The ratio R/r is
A horizontal pipe line carries water in a stream line form. At a point along the pipe where the cross-sectional area is 10 cm 2 , the water velocity is 1 m/s and the pressure is 2000Pa. The pressure of water at another point where the cross-sectional area is 5 cm 2 , is
A cylinder of radius R is filled with water up to a height II, so that the thrust on the walls is equal to that on bottom. The relation between H and R is
A sphere of solid material of relative density 9 has a concentric spherical cavity and Just sinks in water. If the radius of the sphere be R, then the radius of the cavity (r) will be related to R as
The cylindrical tube of a spray pump has a radius,H, one end of which has n fine holes, each of radius r. If the speed of flow of the liquid in the tube is y, the speed of ejection of the liquid through the hole is
The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are v and 2 v respectively. The density of air is p and surface area of wing is A. The dynamic lift on the wing is
A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s) through a small hole on the side of the cylinder near its bottom is
A cylindrical vessel with its axis vertical is filled with a liquid of negligible viscosity to a height z and in its side is a small orifice at a height y, both z and y being measured from the bore. If the jet of liquid strikes the horizontal plane through the base at a distance x from bore, the maximum value of x will be
A tank is filled with water up to a height H. Water is allowed to come out of a hole P in one of the walls at a depth h below the surface of water . Express the horizontal distance x in terms of H and h
The vessel of area of cross-section A has liquid to a height H. There is a hole at the bottom of vessel having area of cross-section a. The time taken to decrease the level from H 1 to H 2 will be
A large tank filled with water to a height i, is to be emptied through a small hole at the bottom. The ratio of time taken for the level to fall from h to h / 2 and that taken for the level to fall from h / 2 to 0 is
A cylinder is filled with non-viscous liquid of density d to a height ho and a hole is made at a height t, from the bottom of the cylinder. The velocity of liquid issuing out of the hole is
A liquid flows in the tube from left to right as shown in fig. (3). A 1 and A 2 , are the cross-sections of the portions of the tube as shown. Then the ratio of speeds v 1 / v 2 willbe
A stream-line body with relative density d, falls into air from a height h, on the surface of a liquid of relative density d 2 where d 2 >d 1 . The time of immersion of the body into liquid will be
A tube of length /r, which is wide enough to male surface tension effects negligible, is closed at one end. It is then lowered into a tank of mercury to a depth.h as shown in fig. (4), so that mercury rises a distance x into the tube. If the mercury barometer stands at i also, then
A vessel contains oil (density =0.8gm/cm 2 ) over mercury (density =13.6gm/cm 2 ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of material of tire sphere in gm/cm 3 is
A body floats with one-third of its volume outside water and 3/4 of its volume outside another liquid. The density of other liquid is
Two solids A and B float in water. It is observed that.A floats with half its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B
An iceberg is floating partially immersed in sea-water The density of sea-water is 1.03 gm/cm 3 and that ice is 0.92 gm/cm 3 . The fraction of the total volume of the iceberg above the level of sea-water is
A spherical ball of radius r and relative density 0.5 is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is Just immersed in water is
A tank of height 5m is full of water. There is a hole of cross-sectional area 1 c m 2 in its bottom. The initial volume of water that will come out from this hole per second is
A uniformly tapering vessel is filled with a liquid of density 900 kg/m 3 The hydrostatic thrust that acts on the base of the vessel due to the liquid is (g =10 m / s 2 )
A wooden ball of density D is immersed in water of density d to a depth h and then released . The height above the surface of water up to which the ball will jump out of water is ( neglect viscous effect )
A liquid is poured into a vessel at rest with the hole in the wall closed. It is filled to a height H. With what horizontal acceleration should the vessel be moved so that the liquid does not come out, when the hole is opened ?
A body of density d 1 is counterpoised by weight Mg of density d 2 in air of density d. Then the true mass of the body is
A body of mass 2 kg is floating in water with half of its volume submerged. What would be the force required to wholly submerge it into water ?
A small cylinder of 2 cm diameter is connected to a large cylinder of 20 cm diameter and each cylinder is fitted with suitable pistons. An incompressible fluid is filled in the cylinders. A force of 60 N is applied to the piston of the small cylinder, then the force exerted on the piston of the large cylinder will be
A cubical block of wood specific gravity 0.5 and chunk of concrete of specific gravity 2 . 5 are fastened together. The ratio of the mass of wood to the mass of concrete, which makes the combination to float with its entire volume submerged under water is
A body of volume v and density p is initially suberged in a liquid of density o. It is lifted through a height h in the liquid. Its potential energy
A concrete sphere of radius fl has cavity of radius r which is packed with saw dust. The specific gravity of concrete and saw dust are respectively 2 . 4 and 0 . 3. For this sphere to float with its entire volume submerged under water, ratio of mass of concrete to mass of saw dust will be
Two identical cylindrical vessels with their bases at same level each contains a liquid of density d. The height of the liquid in one vessel in h 1 , and that in the other vessel is h 2 . The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected is
If V 1 and V 2 be the volumes of the liquids flowing out of the same tube in the same interval of time and n 1 and n 2 their coefficients of viscosity respectively, then
Under a constant pressure head, the rate of flow of orderly volume flow of liquid through a capillary tube is V. If the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become
The rate of flow of a liquid through a capillary tube of radius r is V when the pressure difference is P. If the radius is reduced to r/2 and the pressure increases to 2 P 1 then the rate of flow becomes
16 cm 3 of water flows per second through a capillary tube of radius o cm and of len6h /cm when connected to a pressure head of fi cm of water. If a tube of the same length and radius α /2 cm is connected to the same pressure head, the quantity of water flowing through the tube per second will be
We have two (narrow) capillary tubes T 1 , and T 2 . Their lengths are l 1 and l 2 and radii of cross-sections arc r 1 , and r 2 respectively. The rate of flow of water under a pressure difference P through tube T 1 , is 8 cm 3 /s. If l 1 =2 l 2 and r 1 = r 2 , what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same (P) as before?
A volume V of a viscus liquid flows per unit time due to a pressure head ΔP along a pipe of diameter d and length d/2 and length 2l is connected to the same pressure head ΔP Now the volume of the liquid flowing per unit time is
A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure (6) by
Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is
If the terminal speed of a sphere of gold (density = 19 ⋅ 5 kg / m 3 ) is 0.2m/ s in viscous liquid (density = 1 ⋅ 5 kg / m 3 find the terminal speed of a sphere of silver (density = 10.5kg/m 3 ) of the same size in the same liquid
A lead sphere of mass m falls in a viscous liquid with a terminal velocity v 0 . Another lead sphere of mass 8 m will fall through the same liquid with a terminal velocity
The terminal velocity of small sized spherical body of radius r falling vertically in a viscous Liquid is given by a following proportionality
Two spheres of equal masses but radii R and 2 are allowed to fall in a liquid, the ratio of their terminal velocities is
A ball of density ρ is gently released in a liquid of density o where ρ > o. What will be the acceleration of the free fall of the ball in the liquid ?
Two rain drops of same radius coalesce. Before doing so, each was moving with terminal velocity v. What is the terminal velocity of the single drop so formed ?
A solid ball of volume V is dropped into a viscous liquid. It experiences a viscous drag equal to F. If a solid ball of volume 2 V and of the same material is dropped into the same liquid, the viscous drag will be
A ball of mass m and radius r is released in viscous liquid, The value of its terminal velocity is proportional to
A drop of radius 0 .1 mm and density 10 g/cm 3 falls freely under gravity through a distance ft before entering the water. After entering the water the velocity of the ball does not change. Given that g =10 m / s 2 . What is the value of h ? The viscosity of water =10 x 10 -6 P
Two equal drops are falling through air with a steady velocity of 15 cm/s. If the drops coalesce, the new terminal velocity will be
Water from a tap emerges vertically downwards with an initial speed of 1.0 m/s. The cross-sectional area of the tap is 10 -4 m 2 . Assume that the pressure is constant throughout the stream of water and that the flow is steady, the cross-sectional area of the stream 0.15 m below the tap is
If two soap bubbles of different radii are connected by a tube :
There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius R. If the surface tension of the loop be T, then what will be the tension in the thread ?
The excess of pressure inside the first soap bubble is three times that inside the second bubble. The ratio of volume of the first to second bubble is
Work done to blow a bubble of volume V is W. The work done in blowing a bubble of volume 2 V will be
The heat evolved for the rise of water when one end of the capillary tube of radius r is immersed vertically into water is (assume surface tension = I and density of water to be p)
In a surface tension experiment with a capillary tube water rises up to 0.1 m. If the same experiment is repeated on an artificial satellite, which is revolving around the earth, water will rise in the capillary tube up to a height of
Two soap bubbles coalesce. It is noticed that whilst jointed together, the radii of the two bubbles are a and b where a >b. Then the radius of curvature of interface between two bubbles will be
A small drop of water of surface tension T is squeezed between two clean glass plates so that a thin layer of thickness d and area A is formed between them. If the angle of contact is zero, the force required to pull the plate apart is
A soap bubble (surface tension 30 × 10 − 3 N / m has radius 2 cm. The work done in doubling the radius is
A mercury drop of radius 1 cm is broken into 108 droplets of equal size. The work done is T = 35 × 10 − 2 N / m )
Two soap bubbles have radii in the ratio 2 : 1. What is the ratio of excess of pressure inside them ?
Two spherical soap bubbles of radii r 1 and r 2 in vacuum coalesce under isotherm al conditions. The resulting bubble has a radius R such that
Surface tension of a soap solution is 1 ⋅ 9 × 10 − 2 N / m Work done in blowing a bubble of 2 .0 cm diameter will be
If the surface tension of soap solution is T. what is the work done in blowing soap dabble of radius r ?
Density of ice is ρ and that of water is σ . What will be the decrease in volume when a mass M of ice melts ?
An air bubble is formed at a depth h inside the container of a soap solution of density ρ . If T be the surface tension of the soap solution and P o , the atmospheric pressure, then the total pressure inside the bubble will be
A solid of relative density D is floating in a liquid of relative density d, if v be the volume of the solid submerged in the liquid and V be the total volume of the solid, then
A boat having a length 3 metre and breadth 2 metre is floating on a lake. The boat sinks by one cm when a man gets on it. The mass of the man is
A cylindrical vessel is filled with equal amounts by weight of mercury and water. The overall height of the two layers is 29.2 cm. Specific gravity of mercury is 13 . 6. Then the pressure of the liquids at the bottom of the vessel is
A rectangular vessel when full of water takes 10 minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water ?
If A denotes the area of free surface of a liquid and} the depth of an orifice of area of cross-section o below the liquid surface then the velocity r of flow through the orifice is given by
A wide vessel with a small hole in the bottom is filled with water and kerosene. Neglecting viscosity, the velocity of water flow v, if the thickness of water layer is h 1 and that of kerosene layer is h 2 , is [density of water is ρ 1 , gm/cc and that of kerosene is ρ 2 , gm/cc)
A raft of wood (density 600 kh/m 3 ) of mass 129 kg floats in water. How much weight can be put on the raft to make it just sink ?
A cylinder of mass M and average density d 1 is lowered into a vessel of cross-sectional area A, half full of liquid of density d 2 d 2 < d 1 ) until it is completely covered. The increase in pressure at bottom of vessel is
A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4 y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, R is equal to
When a block of iron floats in mercury at 0 o C, a fraction k 1 , of its volume is submerged, while at the temperature 60 0 C , a fraction k 2 , is submerged. If the coefficient of volume expansion of iron is γ Fe and that of mercury is γ Fe , then the ratio ,k 1 / k 2 can be expressed as
A rectangular box containing water is accelerated upwards at 3 m / s 2 on a inclined plane making 30″ to the horizontal as shown in fig. The side of the free liquid surface is
Air is blown through a pipe AB at the rate of 15 L/min. The cross sectional area of the wide portion of the pipe AB is cm 2 and that of narrow portion is 0.5cm 2 . the difference in water level is ρ air = 1 ⋅ 3 kg / m 3
A solid rubber ball of density p and radius Ii falls vertically through air. Assuming that the air resistance on the ball is F = I .R v, where K is a constant and y is the velocity. Because of this air resistance, the ball attains a constant velocity called terminal velocity v T after some time, then v T is
In a horizontal tube with area of cross-section A 1 and A 2 as shown in fig (5) , the liquid is flowing with velocities v 1 and v 2 respectively. The difference in the levels of the liquid in the two vertical tubes is h. Then
A wooden block, with a coin placed on its top, floats in water as shown in fig. The distances / and i are shown there. After some time, the coin falls into water, then
A large open top container of negligible mass and uniform cross-sectional area A has a small hole of cross-sectional area a in its side wall near the bottom, The container is kept over a smooth horizontal floor and contains a liquid of density p and mass mo. Assuming that the liquid starts flowing though the hole, the acceleration of the container will be
1000 drops of water, all of same size join together to form a single drop and the energy released raises the temperature of the drop. Given that ? is the surface tension of water, r the radius of each small drop, p the density of liquid, / the mechanical equivalent of heat. What is the rise in temperature ?
The surface tension of a soap solution is 0.02 N/m. The work done in blowing a soap bubble of radius 0 .015m is of the order of
Two soap bubbles of radii r 1 and r 2 , r 1 > r 2 get attached to each other to have a common interface. The radius of this interface is
The excess of pressure inside one soap bubble is three times that inside a second bubble’ The ratio of the volume of the first bubble to that of second is
There is a small hole in a hollow sphere. The water enters in it when it is taken to a depth of 40 cm under water. The surface tension of water is 0.07 N/m. The diameter of hole is
A paper disc of radius R from which a hole of radius r is cut out, is floating in a liquid of surface tension T. The force on the disc due to surface tension will be
A metallic wire of density d floats horizontal in water. The maximum radius of the wire such that it may not sink, will be (surface tension of water =T)
A liquid is placed in a vertical cylindrical vessel and the vessel is rotated about its axis, the liquid will take the shape shown in fig. (8)
A solid cube of density p, floats in a liquid of density ρ 1 at 0°C as shown in fig. (2). If γ and f be the coefficient of volume expansion of the liquid and fraction of the cube immersed in the liquid respectively, then the temperature at which the solid will be completely immersed will be
Three vessels A, B and C of different shapes contain a water upto the same height as shown in the figure. P A , P B and P C be the pressures exerted by the water at the bottom of the vessels A, B and C respectively Then
A cemented sphere of radius R has a cavity of radius r which is packed with sawdust. The relative density of cement and sawdust are 2.4 and 0.3 respectively. Find the ratio of mass of cement to sawdust for which the sphere will float in water in completely submerged state.
Mercury Over a Piston: A vertical cylinder of height 100 cm contains air at a constant temperature and its top is closed by a frictionless piston at atmospheric pressure which is 76 cm of Hg column height. If mercury is slowly poured over the top of piston, find the maximum height of mercury column that can be put over piston.
In a wind tunnel experiment, the pressures on the upper and lower surfaces of the wings are 0.90 x 10 5 Pa and 0.91x 10 5 Pa respectively. If the area of the wing is 40 m 2 then the net lifting force on the wing is
A block B of mass 13 kg and base area 1 m x 1m is sliding on an inclined plane lubricated by an oil layer of thickness 0.15 cm. It is observed that block slides with a steady speed of 0.5 m/s. Find viscosity of oil (in Pl). (Take g = 10 m/s 2 )
A thin liquid film formed between a U shaped wire and a light slider supports a weight of 1 .5 × 10 − 2 N , as shown in the figure. The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is
The rate of flow of water through the tube shown is 1000 cm 3 /s. The area of cross-section at point A and B are 10 cm 2 and 4 cm 2 . The difference in mercury level (h) in the tube is cm. g = 10 m / s 2 , ρ Hg = 13600 kg / m 3 , ρ H 2 O = 10 3 kg / m 3
A number of droplets, each of radius r, combine to form a drop of radius R. If T is the surface tension, the rise in temperature will be
Which of the following graph shows the variation of surface tension with temperature over small temperature ranges for water?
A long capillary tube of radius 0.1 cm open at both ends is filled with water and placed vertically. What will be the height of the column of water left in the capillary (in cm)? Given, surface tension of water = 75 dyne cm -1 and density of water = 1 g cm -3 . (Take g = 1000 cm/s 2 )
Two vertical parallel glass plates are partially submerged in water. The distance between the plates is d and the length is l. Assume that the water between the plates does not reach the upper edges of the plates and that the wetting is complete. The water will rise to height ( ρ density of water and σ = surface tension of water)
A cubical block of wood of side a and density ρ floats in water of density 2 ρ . The lower surface of the cube just touches the free end of a massless spring of force constant K fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is
We have two different liquids A and B whose relative densities are 0.75 and 1.0, respectively. If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
A 20-cm-long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
The glycerine of density 1 .25 × 10 3 kgm − 3 is flowing through a conical tube with end radii 0.1 m and 0.04 m respectively. The pressure difference across the ends is 10 Nm -2 . The rate of flow of glycerine through the tube is
There is a hole of area A at the bottom of a cylindrical vessel. Water is filled upto a height h and water flows out in t sec. If water is filled to a height 4h, then it will flow out in time
A wooden ball of density ρ is immersed in water of density ρ 0 to depth h and then released. The height H above the surface of water upto which the ball jump out of water is
An ice cube of size l = 50 cm is floating in a tank (base area A = 2 m × 2 m ) partially filled with water. water is Density of ρ w = 1000 kgm − 3 and that of ice is ρ ice = 900 kg − 3 Calculate change increase in gravitational potential energy (in J) when ice melts completely. (g = 10 ms -2 )
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
