A ball of mass 10 gm dropped from a height of 5m hits the floor and rebounds to a height of 1.25m. If the ball is in contact with the ground for 0.1s, the force exerted by the ground on the ball is (g=10 m/s 2 )
Force F is applied on upper pulley. If F = 30 t, where t is time in second. Find the time (in sec) when m 1 loses contact with floor. (Take g = 10 m/s 2 )
A ball of mass 1 kg hangs in equilibrium from two strings OA and OB as shown in figure. The ratio of tensions in strings OA and OB is : (Take g = 10 ms − 2 )
Two blocks are in contact on a frictionless table. One has mass m and the other 2 m. A force F is applied on 2m as shown in the figure. Now, the same force F is applied from the right on m. In the two cases, the ratio of force of contact between the two blocks will be
A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it
Three equal weights A, B, C of mass 2 kg each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weights, B and C is:
A uniform sphere of weight W and radius 3 m is being held by a string of length 2m.attached to a frictionless wall as shown in the t figure. The tension in the string will be:
Gravel is dropped into a conveyor belt at a rate of 0.5 kg/s. The extra force required in newton to keep the belt moving at 2 m/s is:
A 15 kg block is initially moving along a smooth horizontal surface with a speed of v = 4 m/s to the left. It is acted by a force F, which varies in the manner shown. Determine the velocity of the block at t=15 seconds. Given that, F = 40 cos π 10 t
If block A is moving with an acceleration of 5 m s -2 , the acceleration of B w.r.t ground is
A lift of total mass M is raised by cables from rest through a height h. The greatest tension which the cables can safely bear is nMg. The maximum speed of lift during its journey if the ascent is to made in shortest time is
The masses of 10 kg and 20kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20kg mass. At the instant shown, the 10 kg mass has acceleration 12 m/s 2 . What is the acceleration of 20 kg mass?
In the figure shown, the acceleration of A is 2 m/s 2 to left and acceleration of B is 1 m/s 2 to left. The magnitude of acceleration of C in m/s 2 is
In the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of block C will be
A shell is fired from the ground at an angle θ with horizontal with a velocity ‘v’. At its highest point it breaks into two equal fragments. If one fragment comes back through its initial line of motion with same speed, then the speed of the second fragment will be
A 238 U nucleus decays by emitting an alpha particle of speed v ms − 1 . The recoil speed of the residual nucleus is (in ms − 1 )
A gun fires a bullet of mass 50 gm with a velocity of 30 m sec − 1 . Because of this the gun is pushed back with a velocity of 1 m sec − 1 . The mass of the gun is
A mass of 3 kg descending vertically downwards supports a mass of 2 kg by means of a light string passing over a pulley. At the end of 5 s, the string breaks . How much high from now the 2 kg mass will go? (Take, 9 = 9.8 m s – 2 )
A balloon starting from rest ascends vertically with uniform acceleration to a height of 100 m in 10 s. The force on the bottom of the balloon by a mass of 50 kg is (Take, g = 10 ms -2 ) [EAMCET 2013]
A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off at right angles to each other, one with a velocity 2 i ^ m / s and the other with a velocity 3 j ^ m / s . If the explosion takes place in 10 -5 sec, the average force acting on the third piece in newton is:
A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle θ without changing its speed. The impulse imparted to the ball is given by
A gun of mass 20 kg has bullet of mass 0.1 kg in it. The gun is free to recoil 804 J of recoil energy are released on firing the gun. The speed of bullet (ms -1 ) is
The period of oscillation of a simple pendulum of length l suspended from the roof of the vehicle which moves down without friction on an inclined plane of inclination α , is given by:
A rocket set for vertical firing weighs 50 kg and contains 450 kg of fuel. The product of combustion can have a maximum velocity of 2 km/s. What should be the minimum rate of fuel consumption to give it an acceleration of 20 m / s 2 ? Take g = 9 . 8 m / s 2 .
A chain has mass m and contains n identical links, where n is an odd integer. The chain is hanging vertically from the roof. If g is the acceleration due to gravity, the force exerted by the middle link on the one that is below it is
When three forces of 50 N, 30 N and 15 N act on a body, then the body is
In order to raise a mass m a man ties it to a rope and passes the rope over a frictionless pulley. He climbs the rope with an acceleration 3g/2 relative to the rope. If the mass of the man is m/2 and the mass of the rope is negligible, the tension in the rope is
A particle moves such that its position vector r t = cos ω t i ^ + sin ω t j ^ where ω is a constant and t is time. Then which of the following statements is true for the velocity ν t and a t acceleration of the particle :
A rocket of mass 20kg has 180 kg of fuel. The exhaust velocity of fuel is 1.6 km/sec. Calculate the ultimate velocity of the rocket gained, when the rate of consumption of the fuel is 2kg/sec. (neglect gravity)
A man in a lift feels an apparent weight W when the lift is moving up with a uniform acceleration of 1/3 rd of the acceleration due to gravity. If the same man were in the same lift now moving down with a uniform acceleration that is 1/2 of the acceleration due to gravity, then his apparent weight is
A unidirectional force F varying with time t as shown in the fig. acts on a body initially at rest for a short duration 2T. Then the velocity acquired by the body is
A man thinks to remain in equilibrium by pushing in his hands and feet against two vertical parallel walls as the shown in the figure : a) He must exert equal forces on both walls b) The forces of friction at both walls must be equal c) The coefficients of friction between man and wall must be the same at both ends d) Friction must be present on both walls
The position-time graph of a body of mass 0.04 kg. Suggest a suitable physical context for this motion. The time between two consecutive impulses received by the body, the magnitude of each impulse is
A monkey of mass 15 kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of 1 m/s 2 , how much force should it apply to the rope ? If the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling ?
A body of mass 5kg moving along a straight line is accelerated from 4ms –1 to 8ms –1 with the application of a force of 10N in the same direction. Then,
A varying horizontal force F = a t acts on a block of mass m kept on a smooth horizontal surface. An identical block is kept on the first block. The coefficient of friction between the blocks is μ .The time after which relative sliding between the blocks prevails is
Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2 m? (g is the acceleration due to gravity)
A thin uniform spherical shell and a uniform solid cylinder of the same mass and radius are allowed to roll down a fixed incline without slipping, starting from rest. The ratio t sph t cyl of times taken by them to roll down the same distance is
A block of mass m shown in figure is in equilibrium. If it is displaced downward further by x and released find its acceleration just after it is released. Take pulleys to be light and smooth and strings light.
Consider the situation shown in figure. All the surfaces are smooth. The tension in the string connected to 2 m is
M is a fixed wedge. Masses m 1 and m 2 are connected by a light string. The wedge is smooth and the pulley is smooth and fixed. m 1 = l0 kg and m 2 = 7.5 kg. When m 2 is just released, the distance it will travel in 2 seconds is
Figure shows a man of mass 50 kg standing on a light weighing machine kept in a box of mass 30 kg. The box is hanging from a pulley fixed to the ceiling through a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, the weight shown by the machine is.
A body of mass I kg lies on smooth inclined plane. The block of mass m is acted upon by force F = l0 N horizontally as shown. The magnitude of net normal reaction on the block is:
Water (density ρ )is flowing through the uniform horizontal 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)
Two bodies of masses 5 kg and 4 kg ate arranged in two positions as shown in Figure (A) and (B), if the pulleys and the table are perfectly smooth, the accelerations of the 5 kg body in cases (A) and (B) are:
In Figure (A), mass m is lifted up by attaching a mass 2m to the other end of the string while in Figure (B), m is lifted by pulling the other end of the string with a constant force F = 2mg,then:
consider a system of masses M 1 and M 2 (M 1 > M 2 ) connected by a massless string. In Figure (A), the system is pulled by a force F from the side of mass M 1 and in Figure (B), the system is pulled by the same force F from the side of mass M 2 , then:
In shown figure m 1 = 2kg and m 2 – 4 kg. The pulley is movable. At t = 0, both masses touch the ground and the string is taut. A vertically upward force F = 2t (F is in newton and t is in second) is applied to the pulley” the time when m 2 is lifted off the ground is:
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s 2 , the reading of the spring balance will be :
A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength is 75% of the weight of the monkey; the minimum acceleration with which the monkey can slide down without breaking the branch is:
A gun is mounted on a vehicle which is at rest on a frictionless road. Mass of vehicle + gun is 1600 kg. The gun fires 20 bullets per sec, each with a velocity 400 m/s. Mass of each bullet is 20 gm. Acceleration produced in the vehicle is:
A body of mass 3 kg hits a wall at an angle of 60° and returns at the same angle. The impact time was 0.2 s. Calculate the force exerted on the wall :
A cricketer catches a ball of mass 150 gm in 0. 1 second moving with speed 20 ms -1 , then he experiences force of :
A body of mass 2 kg has an initial velocity of 3 meters per second along OE and it is subjected to a force of 4 N in a direction perpendicular to OE. The magnitude of displacement of the body from O after 4 seconds will be
In the following figure the masses of the blocks A and B are same and each equal to m. The tensions in the strings OA and AB are T 2 and T 1 , respectively. The system is in equilibrium with a constant horizontal force mg on B. Then T 1 is
The acceleration of block B in the figure will be
A U-shaped wire has a rough semicircular bending between A and B as shown in the figure. A bead of mass m moving with uniform speed v through the wire enters the semicircular bend at A and leaves at B with velocity v/2 after time T. The average force, exerted by the bead on the part AB of the wire is
In figure, lower pulley is free to move in vertical direction only. Block A is given a uniform velocity u as shown, what is velocity of block B as a function of angle θ .
A wooden box is placed on a table. The normal force on the box from the table is N 1 . Now another identical box is kept on first box and the normal force on lower block due to upper block is N 2 and normal force on lower block by the table is N 3 . For this situation, mark out the correct statement(s).
A body of mass 2 kg has an initial velocity of 3 meters per second along OE and it is subjected to a force of 4 N in a direction perpendicular to OE. The distance of the body from O after 4 seconds will be
For the pulley system shown in the figure, each of the cables at A and B is given a velocity of 2 ms -1 in the direction of the arrow. Determine the upward velocity v of the load m.
A block of mass m and wedge M is arranged as shown in the figure. Initially the system is kept stationary, certain time system is released from rest. If acceleration of M is found to be A = 5 m / s 2 towards right, then find net acceleration of m with respect to ground
If the blocks are moving as shown in the figure the relation between a 1 , a 2 and a 3 will be
A balloon is tied to a block. The mass of the block is 2 kg. The tension of the string between the balloon and the block is 30 N. Due to the wind, the string has an angle θ relative to the vertical direction, cos θ = 4/5 and sin θ = 3/5. Assume the acceleration of gravity is g = 10 m/s 2 . Also assume the block is small so the force on the block from the wind can be ignored. Then the y-component and the y-component of the acceleration a of the block.
In the figure shown blocks A and B are kept on a wedge C. A, B and C each have mass m. All, surfaces are smooth. Find the acceleration of C.
What force (in N) must man exert on rope to keep platform in equilibrium. (Take g = 10 m / s 2 )
In figure shown, pulleys are ideal. Initially the system is in equilibrium and string connecting m 2 to rigid support below is cut. What is the initial acceleration (in m/s 2 ) of m 2 ? Given m 1 = 9 kg ; m 2 = 3 kg
A block is sliding along inclined plane as shown in figure. If the acceleration of chamber is ‘a’ as shown in the figure. The time required to cover a distance L along inclined plane is
A bomb of mass 9kg explodes into 2 pieces of mass 3kg and 6kg. The velocity of mass 3kg is 1.6 m/s, the K.E. of mass 6kg is
A space craft of mass M is moving with velocity V and suddenly explodes into two pieces. A part of it of mass m becomes at rest, then the velocity of other part will be
A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity 30 meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be
Two blocks of masses m = 5 kg and M = 10 kg are connected by a string passing over a pulley B as shown. Another string connects the centre of pulley B to the floor and passes over another pulley A as shown. An upward force F is applied at the centre of pulley A. Both the pulleys are massless. The accelerations of blocks m and M, if F is 300 N are (Take, g = 10 m s – 2 )
In the diagram shown in figure, string is massless and pulley is smooth, then which of the following statement (s) is/are correct? I. Net force on 1 kg block is 10 3 N II. Net force on both the blocks will be same.
Two bodies of masses 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity g is
Which of the following statement (s) is/are correct? I. A string has a mass m. If it is accelerated, tension is non-uniform and if it is not accelerated, tension is uniform. II. Tension force is an electromagnetic force.
In the diagram shown in figure, all pulleys are smooth and massless and strings are light. Match the following columns. Column I (A) 1 kg block (B) 2 kg block (C) 3 kg block (D) 4 block Column II (p) will remain stationary (q) will move down (r) will move up (s) 5 ms -2 (t) 10 ms -2
A block of mass m is lying on a horizontal surface of coefficient of friction μ . A force F is applied to the block at an angle θ with the horizontal. The block will move with a minimum force F if
Three blocks of masses 3 kg, a kg and 5 kg are connected to each other with light strings and are then placed on a smoot} frictionless surface. Let the system be pulled with a force F from the side of lighter mass so that it moves with an acceleration of 1 m/s 2 . The value of F is
N bullets each of mass m kg are fired with a velocity v rn/s, at the rate of n bullets per second, upon a wall. The reaction offered by the wall to the bullets is
A hammer of mass M strikes a nail of mass m with velocity of u m/s and drives it a metre into a fixed block of wood. The average resistance of wood to the penetration of nail is
A mass M is suspended by a rope from a rigid support at A as shown in fig. Another rope is tied at the end 8, and it is pulled horizontally with a force F. If the rope AB makes an angle q with the vedical, then the tension in the string AB is
A ball of mass m is connected to a ball of mass M by means of a massless spring. The balls are pressed so that the spring is compressed. When released, ball of mass m moves with acceleration a. The magnitude of the acceleration of mass M wiII be
A force of 10 pound is applied on a body of 1 kg. The acceleration of the body is
An explosion blows a rock into three parts. Two pieces go off at right angles to each other; 1.0 kg piece with a velocity of 12 m/s and other 2.0 kg piece with a velocity of 8 m/s. If the third piece flies off with a velocity of 40 m/s, compute the mass of the third piece (in kg).
A body of mass 2kg is acted upon by two forces each of magnitude 1 newton making an angle of 60° with each other. The net acceleration of the body
As shown in figure, if acceleration of M with respect to ground is 2 ms -2 , then
In a football match a ball is kicked by a player with a force of 25 N for 0.2 s and then by another player with a force of 70 N for 0.1 s in the same direction. If the ball gains a velocity of 24 m/s after two kicks, the mass of ball is
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s 2 , the reading of the spring balance will be :
In the Figure given below two masses m and m’ are tied with a thread passing over a pulley, m’ is on a frictionless horizontal surface. If acceleration due to gravity is g, the acceleration of m’ in this arrangement will be:
A block, released from rest from the top of a smooth inclined plane of inclination θ , has a speed v when it reaches the bottom. The same block, released from the top of a rough inclined plane of the same inclination θ , has a speed v/n on reaching the bottom, where n is a number greater than unity. The coefficient of friction is given by
A satellite in force free space sweeps stationary interplanetary dust at a rate dM / dt = αw where M is the mass, v is the velocity of the satellite and a is a constant. What is the decceleration of the satellite?
A horizontal force F is applied on a block of mass m placed on a rough inclined plane of inclination θ . The normal reaction N is
The displacement of a particle executing simple harmonic motion is given by y = A 0 + Asinωt + Bcosωt . Then the amplitude of its oscillation is given by
Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed υ . What is the net force on the block of mass 2m? (g is the acceleration due to gravity)
An object flying in air with velocity ( 20 i ^ + 25 j ^ – 12 k ^ ) suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity ( 100 i ^ + 35 j ^ + 8 k ^ ) . The velocity of the larger piece will be,
In the figure ball A is released from rest when the spring is at its natural length. For the block B of mass M to leave contact with ground at some stage, the minimum mass of A must be
A cannon shell moving along a straight line bursts into two parts. Just after the burst one part moves with momentum 40 Ns making an angle 30 0 with the original line of motion. The minimum momentum of the other part of shell just after the burst is
A 20 gm bullet is shot horizontally and collides with a 1.98 kg block of wood. The bullet embeds in the block and the block slides along a rough horizontal surface for 1.5 m. If the coefficient of kinetic friction between the block and surface is 0.4, the original speed of the bullet is
In outer space, where gravity is zero, a rocket is ejecting gases with a relative velocity of 250 m/s when its total mass is 1500 kg and acceleration of the rocket is found to be 0.5 m / s 2 . Then rate of fuel consumption of the rocket is
Two forces F 1 and F 2 are acting on a body. The body is found to move along positive x-axis with acceleration 3 m / s 2 . When F 2 is reversed, the body is found to move along positive y-axis with acceleration 4 m / s 2 . What will be the acceleration of the body if only F 1 acts on it ?
A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:
A body of mass 4 kg is suspended by a spring balance from the roof of an elevator cage. When the cage is moving up with constant acceleration, reading of the balance is 48 N. When the cage is moving down with same acceleration, reading of the spring balance is g = 10 m / s 2 .
Three forces P, Q and R are acting on a particle in the plane, the angle between P and Q and that between Q and R are 150 0 and 120 0 respectivley . Then for equilibrium, forces P, Q and R are in the ratio
In the arrangement shown, the blocks are released from rest. If magnitude of acceleration of each block is g/4, the ratio M m is
Three equal weights A, B and C of mass 3 kg each are hanging on a string passing over a fixed pulley which is frictionless as shown in figure. The tension in the string connecting B and C is?
A boy is hanging from the free end of a massless rope of length 40 m. The mass of the boy is 20 kg and the maximum tension that the rope can bear is 300 N. Then starting from rest, the minimum time in which the boy can climb the other end of the rope is g = 10 m / s 2
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate d M t d t = b υ 2 t , where υ t is its instantaneous velocity. The instantaneous acceleration of the satellite is:
If ‘O’ is at equilibrium then the values of the tension T 1 and T 2 are x, y, if 20 N is vertically down. Then x, y are
A boy is hanging from a horizontal branch of a tree. The tension in the arms will be maximum, when the angle between the arms is
Two10 kg bodies are attached to a spring balance as shown in figure. The reading of the balance will be
Ten coins each of mass 10 gm are placed one above the other. The reaction force exerted by 7 th coin from the bottom on the 8 th coin is (g = 10 m/s 2 )
A boy of mass 40 kg climbs up a rope with an acceleration of 2 ms –2 . What is the tension in the rope ?
A particle of a small mass m is joined to a very heavy body by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is
A person of mass 72 kg sitting on ice pushes a block of mass of 30 kg on ice horizontally with a speed of 12 ms -1 . The coefficient of friction between the man and ice and between block and ice in 0.02. If g =10 ms -2 , the distances between man and the block, when they come to rest is
A lift is going up, the total mass of the lift and the passengers is 1500 kg. The variation in the speed of lift is shown in fig. Then the tension in the rope at t = 1 s will be
A pendulum is hanging from the ceiling of a cage. When the cage is moving up with certain acceleration and when it is moving down with the same acceleration, the tensions in the strings are T 1 and T 2 respectively. When the cage moves horizontally with the same acceleration, the tension in the string is
Consider the system shown in figure. The pulley and the string are light and all the surface are frictionless. The tension is the string is (Take g = 10m/s 2 )
A 6 kg and 3 kg blocks are connected by a light string that passes over a very light frictionless pulley. The pulley is suspended by a light spring balance. Then reading of the spring balance is
A body of 2 kg has an initial speed 5 ms – 1 . A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The final speed of the body is
An elevator and its load have a total mass of 800kg. The elevator is originally moving downwards at 10 m s – 1 , it slows down to stop with constant acceleration in a distance of 25m. Find the tension T in the supporting cable while the elevator is being brought to rest. (Take g = 10 m s – 2 )
The figure shows the part of a horizontally stretched net. String AB is pulled with a force of 10N. The tensions in the sections BC and BF when the net is in equilibrium are
A rod of length l slides down along the inclined wall as shown in figure. At the instant shown in figure the speed of end A is v, then the speed of B will be
Three blocks A, B and C of masses 4 kg, 2 kg and I kg respectively are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and.B is
A particle of mass 1 kg is moving on a circular path of radius 1 m. Its kinetic energy is K=bt 4 , where b= 1 J/s. The force acting on the particle at t = 1s is (2x) ½ N. The value of x is .
According to Newton’s second law of motion, resultant force on a particle is in the direction of acceleration of the particle. Two forces F 1 and F 2 are acting on a particle as shown in the figure. The acceleration of the particle is along X-axis. The value of F 1 (in newton) is
A block ‘A’ of mass ‘m’ is attached at one end of a light spring and the other end of the spring is connected to another block ‘B’ of mass 2 m through a light string as shown in the figure.’A’ is held and B is in static equilibrium. Now A is released. The acceleration of A just after that instant is ‘a’. In the next case, B is held and A is in static equilibrium. Now when,B is released, its acceleration immediately after the release is ‘b’. The value of a/b is: (Pulley, string and the spring are massless)
The ratio of acceleration of pulley to the acceleration of the block is (string is inextensible)
ln the arrangement shown in figure the ends P and Q of an non-stretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed
Two masses of I kg and 5 kg are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a light spring balance as shown in figure. The masses start moving during this interval; the reading of spring balance will be:
A block of mass 5 kg is suspended by a massless rope of length 2 m from the ceiling. A force of 50 N is applied in the horizontal direction at the midpoint P of the rope, as shown in the figure. The angle made by the rope with the vertical in equilibrium is (Take g = 10 ms – 2 )m
A 40 kg slab rests on a frictionless floor as shown in the figure. A 10 kg block rests on the top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic coefficient of friction is 0.40. The 10 kg block is acted upon by a horizontal force 100 N. If g = 10 m/s 2 , the resulting acceleration of the slab will be
The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be
A block of mass m is connected to a peg at point D through a light and inextensible string of length 18 m. The length of section AB is 3 m. The point C of string is pulled down by applying a force F of 128 N. Block A remains stationary. If the mass of block A is 16 n kg, the value of n is
The figure shows the force versus time graph for a particle. Then
A puck is moving in a circle of radius r with a constant speed V 0 on a level frictionless table. A string is attached to the puck which holds it in the circle. The string passes through a frictionless hole and is attached on the other end to a hanging object of mass M. The puck is now made to move with a speed v = 3 v 0 but still in circle. The mass of the hanging object is left unchanged. The acceleration a of the puck and the radius r of the circle are now given by (a 0 is the initial acceleration of the puck)
A man of mass 60kg is standing on a platform of mass 20kg suspended with the help of rope pulley arrangement as shown in figure. If he pulls the rope and applies 400N force on the platform then acceleration of the system will be (use g=10m/s 2 )
A 3 kg block A is placed on the top of a 4 kg block B as shown. To make the block A slip on B, assuming frictionless table, a horizontal force of 9 N is to be applied to the top block. Find the minimum horizontal force (in N) that can be applied to lower block so that A slips on B.
A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force F is applied at one end of the rope, the force which the rope exerts on the block is:
In the system shown in Figure, the pulley is frictionless and the string mass less. if m 1 ≠ m 2 , thrust on the pulley is:
A 5 kg weight is accelerated from rest to 60 m/s in 1 sec. What force acts on it?
The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is :
A balloon of gross weight W newton descends with an acceleration f m/s 2 . The weight that must be thrown out in order to give the balloon an equal upward acceleration will be:
In Figure, tension in the string that connects the masses A and B is T 1 and that in the string connecting B and C is T 2 , then T 1 /T 2 is:
In Figure, a sphere of mass 2kg is suspended from the ceiling of a car which is initially at rest. Tension in the string in this situation is T 1 . The car now moves to the right with a uniform acceleration and the tension in the string is now T 2 , then: (Take g = 10 m/s 2 )
On the floor of an elevator, a block of mass 50 kg is placed on which another block of mass 20 kg is also placed. The elevator is moving up with a constant acceleration 1.5 m/s 2 . Force exerted by 20 kg block on the 50 kg block is nearly:
A lift of mass 1000 kg which is moving with acceleration of 1 m/s 2 in upward direction, then the tension developed in string which is connected to lift is :
A ball weighing 10 g hits a hard surface vertically with a speed of 5 m/s and rebounds with the same speed. The ball remains in contact with the surface for 0.01 sec. The average force exerted by the surface on the ball is:
During the rocket propulsion, gases ejecting with velocity 1 km/s relative to rocket. The rate of fuel consumption is m 10 kg / s ,where m is the instantaneous mass of the rocket. If air resistance varies according to equation f – 0.15 mv, then terminal velocity of the rocket is :
A force-time graph for the motion of a body is shown in Figure. change in linear momentum between 0 and g s, is:
A particle moves in the x-y plane under the influence of a force such that its linear momentum is p ( t ) = A [ i ^ cos ( kt ) − j ^ sin ( kt ) ] , where A and k are constants. Angle between the force and the momentum is:
A string is wrapped round a log of wood and it is pulled with a force F as shown in the figure. Choose the correct statement(s) I. Tension T in the string decreases with increases in θ . II. Tension T > F if θ > π /3
Consider three blocks A,B and C. Block A is placed on block B, which is placed on block C and block C is placed on the ground. Normal reaction between blocks B and C is three times of that between blocks A and B. Normal reaction between block C and ground is two times of that of between blocks B and C. Possible values of the masses of blocks A , B and C respectively are :
A system consists of three masses m 1 ,m 2 and m 3 connected by a string passing over a pulley P. The mass ml hangs freely and m 2 and m 3 are on a rough horizontal table (the coefficient of fiction = μ ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m 1 is : (Assume m 1 = m 2 = m)
A wagon of 200 kg is moving on a smooth track with velocity of 2 m/sec. A man of 80 kg also runs in the wagon with a velocity such that speed of the centre of mass of the system is zero. Find the velocity of man relative to the wagon (in m/s).
A body is slipping from an inclined plane of height h and length l. If the angle of inclination is θ , the time taken by the body to come from the top to the bottom of this inclined plane is
N bullets each of mass m kg are fired with a velocity v ms -1 at the rate of n bullets per second upon a wall. The reaction offered by the wall to the bullets is given by
Two skaters have weight in the ratio 4 : 5 and are 9 m apart, on a smooth frictionless surface. They pull on a rope stretched between them. The ratio of the distance covered by them when they meet each other will be
A particle of mass 2kgmoves with an initial velocity of ( 4 i ^ + 2 j ^ ) ms − 1 on the x-y plane. A force F = ( 2 i ^ − 8 j ^ ) N acts on the particle. The initial position of the particle is (2 m,3 m). Then for y=3 m,
A body A of mass m 1 exerts a force on another body B of mass m 2 . If the acceleration of .B be a 2 , then the acceleration (in magnitude) of A is
Five forces F 1 , F 2 , F 3 , F 4 and F 5 are acting on particle of mass 2.0 kg so that it is moving with 4 m/s 2 in east direction. If F 1 force is removed, then the acceleration becomes 7 m/s 2 in north, then the acceleration of the block if only F 1 is acting will be
A particle moves in the xy-plane under the action of a force F such that the components of its linear momentum p at any time t are p x = 2 cos t , p y = 2 sin t . The angle between F and p at time t is
Three blocks A, B, and C are suspended as shown in the figure. Mass of each of blocks A and B is m. lf the system is in equilibrium, and mass of C is M, then
In each of the three arrangements, the block of mass m 1 is being pulled left with constant velocity. There is no friction anywhere. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass m 2 in the three cases respectively is:
Figure shows a 5 kg ladder hanging from a string that is connected with a ceiling and is having a spring balance connected in between. A boy of mass 25 kg is climbing up the ladder at acceleration 1 m/s 2 . Assuming the spring balance and the string to be massless and the spring to show a constant reading, the reading of the spring balance is (Take g = 10 m/s 2 )
A force F = bt (where b is a constant) is applied at an angle to a mass m kept on a smooth horizontal plane. The velocity of mass m at the moment of its breaking off the plane is
Two massless rings slide on a smooth circular loop of the wire whose axis lies in a horizontal plane. A smooth massless inextensible string passes through the rings, which carries masses m 1 and m 2 at the two ends and mass m 3 between the rings. If there is equilibrium when the line connecting each ring with centre subtends an angle 30 o with vertical as shown in figure. Then the ratio of masses are
In the previous question surface is replaced by block C of mass m as shown in the figure. In this case the acceleration of block B is found to be 3 F n m m / s 2 . The value of n is .
A block B of mass 1 kg is placed on a light plank shown in figure. A force F of 10 N is applied on the plank horizontally. Find the acceleration (in m/s 2 ) of block B.
All surfaces are smooth. Find acceleration of triangular in m/s 2 . (Take g = 9 m / s 2
All surfaces are smooth. Find acceleration of triangular in m/s 2 . (Take g = 9 m / s 2
Blocks A and B of masses 2kg and 1 kg respectively are pushed up a frictionless slope by a 21 N force applied parallel to the slope as shown in the figure. Find the magnitude (in newtons) of the force of normal reaction between A and B. g = 10 m / s 2
At t=0, the lower end of the bar A is just above the upper end of bar B (mass of bar A=3 kg, mass of bar B = 11 3 kg). Find time (in sec) when upper end of block A just crosses the lower end of .8. (Assume the system was released at t=0). g = 10 m / s 2
Two monkeys M 1 and M 2 of equal mass ‘m’ can climb strings of a pulley arrangement as shown in figure. Find magnitude of acceleration (in m/s 2 ) of M 1 with respect to rope so that block remains stationary. It is given that M 2 is just holding the string. Assume pulley is frictionless and string is massless and inextensible.
A block of mass 3kg which is on a smooth inclined plane making an angle of 30° to the horizontal is connected by cord passing over light frictionless pulley to second block of mass 2kg hanging vertically. What is the acceleration of each block and what is the tension of the cord?
A body with mass 5 kg is acted upon by a force F = ( − 3 i ^ + 4 j ^ ) N .If its initial velocity at t = 0 is v = ( 6 i ^ − 12 j ^ ) ms − 1 ,then the time at which it will just have a velocity along x-axis is
If ‘O’ is at equilibrium then the values of the tension T 1 and T 2 respectively.
The pulley arrangements shown in the figure are identical, the mass of the rope being negligible. In case (a) mass m is lifted by attaching a mass of 2 m to the other end of the rope. In case (b) the mass m is lifted by pulling the other end of the rope with a constant downward force F = 2 mg, where g is the acceleration due to gravity. The acceleration of mass m in case (a) is :
A steel wire can withstand a load up to 2940N. A load of 150kg is suspended from a rigid support. The maximum angle which the wire can be displaced from the mean position , so that the wire does not break when the load passes through the position of equilibrium is
What is the magnitude of the total force on a driver by the racing car he operates as it accelerates horizontally along a straight line from rest to 60m/s in 8.0s (mass of the driver=80kg)
The position-time graph of a body of mass 0.04kg is shown in the figure. The time between two consecutive impulses received by the body and the magnitude of each impulse is
In an explosion a body at rest breaks up into two pieces of unequal masses. In this
From a stationary tank of mass 125000 pound a small shell of mass 25 pound is fired with a muzzle velocity of 1000 ft/sec. The tank recoils with a velocity of
A shell initially at rest explodes into two pieces of equal mass, then the two pieces will
A cannon ball is fired with a velocity 200 m/sec at an angle of 60° with the horizontal. At the highest point of its flight it explodes into 3 equal fragments, one going vertically upwards with a velocity 100 m/sec, the second one falling vertically downwards with a velocity 100 m/sec. The third fragment will be moving with a velocity
A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be
A block of mass m is placed on a smooth plane inclined at an angle θ with the horizontal. The force exerted by the plane on the block has a magnitude
In the figure shown, a person wants to raise a block lying on the ground to a height h. In both the cases, if time required is the same, then in which case, he has to exert more force. (Assume pulleys and strings are light)
A car of mass m starts from rest and acquires a velocity along east v = v i ^ ( v > 0 ) in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is
A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m s – 1 . To give an initial upward acceleration of 20 m s – 2 , the amount of gas ejected per second to supply the needed thrust will be (Take, 9 = 10 m s – 2 )
If the coefficient of friction between A and B is μ , the maximum acceleration of the wedge A for which B will remain at rest with respect to the wedge is
A balloon of weight w is falling vertically downward with a constant acceleration a (< g). The magnitude of the air resistance is
A dynamometer D is attached to two bodies of masses M = 6kg and m = 4 kg. Forces F = 20N and f = 10N are applied to the masses as shown. The dynamometer reads
A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string (i.e. angle θ ) when the trolley rolls up a plane of inclination α with acceleration a is
Assertion : A glass ball is dropped on concrete floor can easily get broken compared, if it is dropped on wooden floor. Reason : On concrete floor, glass ball will take less time to come to rest. [AIIMS 2019]
A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be
Three blocks A , B and C of masses 4 kg, 2 kg and 1 kg respectively are in contact on a frictionless surface as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is
A 60 kg mass is pushed with a enough force to start it moving and the same force is continued to act afterwards. If the coefficient of static friction and sliding friction are 0.5 and 0.4 respectively, then the acceleration of the body will be [BCECE (Mains) 2012]
A monkey of mass 25 kg is holding a vertical rope. The rope does not break, if a body of mass 30 kg is suspended from it, but the rope breaks, if the mass of the body suspended with the rope exceeds 30 kg. What will be the maximum acceleration with which the monkey can climb up along the rope? (Take, g = 10 m s – 2 ) [JCECE 2012]
A rocket with a lift-off mass 3.5 x 10 4 kg is blast upward with an initial acceleration of 10 m s – 2 . Then, the initial thrust of the blast is [AIIMS 2012]
A man of mass 60 kg is riding in a lift. The weight of the man when the lift is accelerating upwards and downwards at 2 m s – 2 are respectively (Take, g = 10 m s – 2 ) [AMU 2011]
N bullets each of mass m kg are fired with a velocity v ms -1 at the rate of n bullets per second, upon a wall. The reaction offered by the wall to the bullets is given by
A body is moving down a long inclined plane of angle of inclination θ . The coefficient of friction between the body and the plane varies as μ = 0 .5 x , where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by x = N tan θ . The value of N is
The over-bridge of a river is in the form of a circular arc of radius of curvature 10 m. If g = 10 ms -2 . The highest speed (in m/s) at which a motor cyclist can cross the bridge without leaving the ground is
Three equal weights A, B, C of mass 2 kg each are hanging on a string passing over a fixed frictionless pulley as shown in the fig. (3). The tension in the string connecting weights B and C is
A machine gun is mounted on a 2 quintal vehicle on a horizontal smooth road. (Friction negligible). The gun fires 10 bullets per second with a velocity of 500 no/s. If the mass of each bullet be 10 g, what is the acceleration produced in the vehicle?
A block of mass M is pulled along horizontal frictionless surface by a rope of mass m. Force p is applied at one end of rope Fig. The force which the rope exerts on the block is
A constant force F = m 2 g / 2 is applied on the block of mass m, as shown in fig. The string and the pulley are light and the surface of the table is smooth The acceleration of m 1 is
A ship of mass 3 x 10 7 kg initially at rest is pulled by a force of 5x 10 4 N through a distance of 3 m. Assuming that the resistance due to water is negligible, what will be the speed of the ship ?
A solid rubber ball of density d and radius E falls vertically through air. Assume that the air resistance acting on the ball is F = kRV, where k is constant and V its velocity. Because of this air resistance, the ball attains a constant velocity called terminal velocity V t after some time. Then V t is
A house directs a horizontal jet of water moving with a velocity of 20 m/s on to a vertical wall. The cross-sectional area of the jet is 5 x 10 -4 m 2 . If the density of water is 1000 kg / m 3 , the force on the wall assuming that the water comes to rest after striking the wall, is
Two balls A and B of mass 0.10 kg and 0.25 kg respectively are connected by a stretched spring of negligible mass and placed on a smooth table when the balls are released simultaneously, the initial acceleration of ball B is 10 cm/s 2 westward. The magnitude and direction of acceleration of the ball A are
The time period of simple pendulum of length l as measured in an elevator descending with acceleration g/3 is
Two weights W, and W, are attached to the ends of a string which passes over a frictionless pulley. If the pulley is placed in a rocket accelerating upwards at 9.8 m/s 2 , the tension in the string would be (take g = 9.8 m/s 2 )
A hammer of mass M strikes a nail of mass m with velocity of u m/s and drives it a metre into fixed block of wood. The average resistance of wood to the penetration of nail is
A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end as shown in fig. The acceleration of the system is (g = 10 m/s 2 )
At some instant, acceleration of 5 kg is 10 m/s 2 (see fig.). The acceleration of 10 kg at the instant is
A rod of length L and mass M is acted on by two unequal force F1 and F2 (< F1) as shown in fig. The tension in the rod at a distance x from end B will be
A mass of 1 kg is attached to the middle of a rope, which is being pulled from both the opposite directions. Taking g – 10 m/s 2 , what is the minimum pull required to completely straighten the rope ?
A body with mass 5kg is acted upon by a force f = ( − 3 i ^ + 4 j ^ ) N . If its initial velocity at t=0, v = ( 6 i ^ − 12 j ^ ) ms − 1 , the time at which it will just have a velocity along the y axis is
A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes an angle of 60° with the vertical. The new reading of the balance is
A hose directs a horizontal jet of water moving with a velocity of 20 m/sec on to a vertical wall. The cross sectional area of the jet is 5 x 10 –4 m 2 . If the density of water is 10 3 kg/m 3 , find the force on the wall assuming that the water is brought to rest there
A dish of mass 10 g is kept floating horizontally in the air by firing bullets each of mass 5 g with the same velocity. If 10 bullets are fired per second and the bullets rebound with the same velocity, then the velocity of each bullet is
A particle of mass 2kg initially at rest. A force acts on it whose magnitude changes with time. The force-time graph is shown below. The velocity of the particle at t=10 sec is
An object of mass 5 kg is moving with a constant velocity of 10 m s -1 . A constant force acts on it opposite to its velocity 4 seconds and gives it a velocity of 2 m s -1 in the opposite direction. The acceleration produced by the force is
A particle of mass 2kg initially at rest. A force acts on it whose magnitude changes with time. The force-time graph is shown below. The velocity of the particle at t=10 sec is
A cricket player catches a ball of mass 10 -1 kg, moving with a velocity of 25 ms -1 . If the ball is caught in 0.1 s, the force of the blow exerted on the hand of the player is
A body of mass 2 kg moving on a horizontal surface with an initial velocity of 4 m/sec comes to rest after 2 sec. If one wants to keep this body moving on the same surface with a velocity of 4 m/sec, the force required is
A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (g=10m/s 2 )
A rocket of initial mass 6000 kg ejects mass at constant rate of 200 kg/sec. with constant relative speed of 800 m/sec. The acceleration of the rocket after 5 sec is (neglect gravity)
A bullet of mass 10 -3 kg strikes an obstacle and moves at 60° to its original direction. If its speed also changes from 20 m/s to 10 m/s , the magnitude of the impulse acting on the bullet is
A jet of liquid of cross-sectional area a strikes a wall making angle θ with the wall. The water strikes with the wall with velocity v and rebounds elastically. If density of liquid be ρ the normal force on the wall is
Two masses m 1 = 5 kg and m 2 = 4.8 kg tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when they are free to move (g = 9 . 8 m / s 2 )?
If force on a rocket having exhaust velocity of 300 m/sec is 210 N, then rate of combustion of the fuel is
Two blocks are in contact on a frictionless table. One has mass m and the other 2 m. A force F is applied on 2m as shown in the figure. Now, the same force F is applied from the right on m. In the two cases, the ratio of force of contact between the two blocks will be
The rate of mass of the gases emitted from rear of a rocket is initially 0 .1 kgs − 1 . If the speed of the gas relative to the rocket is 50 m/s and mass of the rocket is 2 kg, then the acceleration of the rocket is
In a rocket the mass of the fuel is 90% of the total mass. The rocket is blasted from the launching pad. If the exhaust gases are ejected at a rate of 500 ms − 1 what is the maximum speed attained by the rocket ? Neglect the effects of gravity and air resistance.
A rocket, set for vertical launching has a mass of 50 kg and contains 450 kg of fuel. It can have a maximum exhaust speed of 1 Kms − 1 . If g = 10 ms − 2 What should be the minimum rate of fuel consumption to just lift it off the launching pad.
A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be
Two masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant when the 10 kg mass has an acceleration of the acceleration of 12 ms − 2 , the 20 kg mass is
A mass of 10 kg is suspended by a rope of length 2.8 m from a ceiling. A force of 98 N is applied at the mid-point of the rope as shown in figure. The angle which the rope makes with the vertical in equilibrium is
A block is dragged on a smooth plane with the help of a rope which moves with a velocity as shown in figure. The horizontal velocity of the block is
A rod of length L and mass M is acted on by two unequal forces F 1 and F 2 (> F 1 ) as shown in the following figure The tension in the rod at a distance y from the end A is given by
A rod of length L and mass M is acted on by two unequal forces F 1 and F 2 (> F 1 ) as shown in the following figure The tension in the rod at a distance y from the end A is given by
Two masses A and B of 5 kg and 6 kg respectively are Connected by a string passing over a frictionless pulley fixed at the corner of table as shown in the figure. The coefficient of friction between A and the table is 0.3. Find the minimum mass of C (in kg) that must be placed on A to prevent it from moving (Take g = 10 m/s 2 ).
A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is
The monkey B shown in figure is holding on to the tail of the monkey A which is climbing up a rope. The masses of the monkeys A and B are 5 kg and 2 kg respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry the monkey B with it? (Take, g = 10 ms -2 )
For the system shown in figure, the pulleys are light and frictionless. The tension in the string will be
If force on a rocket having exhaust velocity of 300 m/sec is 210 N, then rate of combustion of the fuel is
A rocket with a lift-off mass 3 .5 × 10 4 kg is blasted upwards with an initial acceleration of 10 m / s 2 . Then the initial thrust of the blast is
A man 80kg is supported by two cables as shown in the figure. Then the ratio of tensions T 1 and T 2 is
For the system shown in figure, the pulleys are light and frictionless. The tension in the string will be
Figure below shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1ms –2 . If the coefficient of static friction between the man’s shoes and the belt is 0.2, upto what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg).
A rocket of initial mass 6000 kg ejects mass at constant rate of 200 kg/sec. with constant relative speed of 800 m/sec. The acceleration of the rocket after 5 sec is (neglect gravity)
A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity V = ( 5 i ^ + 2 t j ^ ) m / s . Here t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take g = 10 m / s 2 )
Two weights w 1 and w 2 are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up at an acceleration g, the tension in the string will be
The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8s is
A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a ?
A body of mass ‘m’ is released from rest on an inclined plane in an elevator (moving up with acceleration a 0 ). Find the time taken by the body to reach the bottom of the inclined plane.
A block of mass m is placed on a smooth inclined wedge A B C of inclination θ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is
A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.4, the magnitude of the frictional force acting on the block is
A ship of mass 3 × 10 7 kg initially at rest is pulled by a force of 5 × 10 4 N through a distance of 3 m. Assume that the resistance due to water is negligible, the speed of the ship is
Boy is pulling the rope as shown below. Reading of the weighing machine is
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m s − 1 and the second part of mass 2 kg moves with 8 m s − 1 speed. If the third part flies off with 4 m s − 1 speed, then its mass is
Three blocks A, B and C , of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is
A block is released from rest from point A on a smooth track, whose cross section in vertical plane is quarter of a circle of radius ‘R’. The value of θ for which the contact force between block and surface is equal to the weight of block is
A block A of mass m 1 rests on a horizontal table. A light string connected to it passes over a frictionless pully at the edge of table and from its other end another block B of mass m 2 is suspended. The coefficient of kinetic friction between the block and the table is μ k . When the block A is sliding on the table, the tension in the string is
Figure shows two blocks A and B connected to an ideal pulley string system. In this system when bodies are released then: (neglect friction and take g = 10 m / s 2 )
A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 m s – 1 . The final velocity acquired by the person and the average force exerted on the person are
Two identical springs of constant k are connected in series and parallel as shown in figure. A mass M is suspended from them. The ratio of their frequencies of vertical oscillations will be:
A small block of mass m rests on a smooth wedge of angle θ . With what horizontal acceleration ‘ a’ should the wedge be pulled, as shown in Fig., so that the block falls freely?
Two bodies of mass 4 kg and 6kg are tied to the ends of a maasless string. The string passes over a pulley which is frictionless (see figure). The accleration of the system in terms of acceleration due to gravity (g) is :
A particle of mass 2kg initially at rest. A force acts on it whose magnitude changes with time. The force-time graph is shown below. The velocity of the particle at t=10 sec is
Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is 0.05. ( g = 10 m / s 2 , mass of the string is negligible and no other friction exists).
A stone weighing 1 kg and sliding on ice with a velocity of 4 m/s is stopped by friction in 30 sec. The force of friction (assuming it to be constant) will be
A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. The pendulum will tilt
Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ . They are brought in contact and separated. What will be the new surface charge densities on them?
A particle of mass 5m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular direction with speed v each. The energy released during the process is,
An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with X in the manner shown. The velocities of the object at the points X = 8 m and X = 12 m, would have the respective values of (nearly)
A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination 30°. The centre of mass of the cylinder has speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be, [ take g = 10 m / s 2 ]
A spring – mass system is hanging from the ceiling of an elevator in equilibrium. The elevator suddenly starts accelerating upwards with acceleration 5 m / s 2 . If mass of the block is 1 kg and force constant of the spring is 1000 N/m, the amplitude of oscillation is
At a certain moment of time, velocities of 1 and 2 both are 1 m/s upwards. Find the velocity of 3 at that moment.
A block attached between two springs is in equilibrium. If the upper spring is cut, then the acceleration of the block just after cut is 6 m/s 2 downwards. Now, if instead of upper spring, the lower spring is cut, then the magnitude of acceleration of the block, just after the cut will be (Take g = 10 m/s 2 and identical springs)
With what minimum acceleration should the wedge move horizontally for which the block B falls freely Take g = 10 m / s 2
A chain of mass m is attached at points A and B of a ceiling. Due to its own weight, a sag is there as shown. Then tension at lowest point C is
A lift is going up. The total mass of the lift and the passenger is 1500 kg. The variation in the speed of the lift is as shown in the graph. The tension in the rope of the lift at t = 11 th second will be
Linear momentum of a body is given by p = ( 20 t – 3 t 2 ) kg – m / s . Then the force acting on the body at t = 1 sec,is
A balloon of mass M is descending at a constant acceleration α . When a mass m is released from the balloon, it starts rising with the same acceleration α . Assuming that its volume does not change, what is the value of m ?
A block A has a velocity of 0.6 m s – 1 to the right. Determine the velocity of cylinder B.
A block of mass m is placed on a smooth wedge of inclination θ . The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ( g is acceleration due to gravity) will be
The acceleration of the 2 kg block if the free end of string is pulled with a force of 20 N as shown is
Gravels are dropped on a conveyor belt at a rate of 0.5 kg/s. The extra force required in newtons to keep the belt moving at 2 m/s is
A stationary body of mass 3kg explodes into three equal pieces. Two of the pieces fly off at at right angles to each other, one with a velocity 2 i ^ m / s and the other with a velocity 3 j ^ m / s . If the explosion takes place in 10 – 5 s e c , the average force acting on the third piece in newton is
A light string passing over a smooth light pulley connects two blocks of masses m 1 and m 2 (vertically). If the acceleration of the system is g/8 then the ratio of the masses is
For the pulley system shown in Fig. , each of the cables at A and B is given a velocity of 2 m s – 1 in the direction of the arrow. Determine the upward velocity v of the load m.
A bead of mass m is released from rest at A to move along the fixed smooth circular track as shown in Fig. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point P 0 described by the angle θ ( ≠ 0 ) would
A machine gun fires a steady stream of bullets at the rate of n per minute into a stationary target in which the bullets get embedded. If each bullet has a mass m and arrives at the target with a velocity v, the average force on the target is :
A mass of 10 kg is suspended by a rope of length 4m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45º with the vertical. Then F equals: (Take g = 10 m s – 2 and the rope to be massless)
A body of mass 2 kg moves along x-axis under the influence of a force which varies with time according to the graph shown in figure. Then average acceleration of the body is
A block on table (weight 40 N) shown in figure is just on the wedge of slipping. Find the coefficient of static friction between the block and table (weight of the hanging mass is 60 N )
In the diagram shown the table top is rough and coefficient of friction between any of the blocks and table top is μ . The blocks A and B are on the verge of slipping. If position of the blocks A and B are interchanged and the system is released from rest, then acceleration of the blocks is
A stationary object explodes into two fragments of masses 2 kg and 4 kg. Just after the explosion, velocity of the smaller fragment is found to be 8 m/s. Then kinetic energy of the larger fragment just after explosion is
The system shown in the figure is released from rest. At the instant when mass M has fallen through a distance h, the velocity of m will be
A spring mass system ( mass m , spring constant k and natural length l ) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the center of the disc. If the disc together with spring mass system, rotates about it’s axis with an angular velocity ω , k > > m ω 2 the relative change in the length of the spring is best given by the option
Mass of an empty rocket is 50 kg and mass of its fuel is 100kg. The rocket is fired on the surface of earth. If initial rate of consumption of fuel is 2 kg/s and velocity of exhaust gas relative to the body of the rocket is 800 m/s, Find the initial acceleration of the rocket
A body is in equilibrium under the action of three coplanar forces P, Q and R are shown in the figure. Select the correct statement.
As shown in figure the tension in the horizontal cord is 30 N. The weight W and tension in the string OA (in newton) are
A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong?
A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y = 4 c x 2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction):
Normal reaction N is a force exerted by the surface on the block perpendicular to the surface of contact. A block of mass 1 kg is placed on inclined plane of inclination 37 0 as shown in the figure . Find the component of normal reaction N = 8 N on the block x-axis and y-axis.
A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force m k ν 2 where ν is its speed. The maximum height attained by the ball is:
A body of mass √3 kg is suspended by a string to a rigid support. The body is pulled horizontally by a force F until the string makes an angle of 30° with the vertical. The value of F and tension in the string are.
When forces F 1 , F 2 , F 3 are acting on a particle of mass m such that F 2 and F 3 are mutually perpendicular, then the particle remains stationary, If the force F 1 is now removed then acceleration of the particle is
From the figure, if the mass is at equilibrium then find T 1 and T 2
The area under force time curve gives
A fat hose pipe is held horizontally by a fireman. It delivers water through a constricting nozzle at 1 litre/sec. If by increasing the pressure, the water is delivered at 2 litre/sec, the fireman now has to
A force is applied for a duration of 10 sec on a body of mass 5 kg that is at rest. As a result the body acquires a velocity of 2 ms –1 . Find the magnitude of the average force applied.
If action force acting on a body is gravitational in nature, the reaction force
A boy holds a rubber ball in his hand. The reaction force of gravity on the ball is the force exerted by the
A force of 25 N acts on a body at rest for 0.2 s and a force of 70 N acts for the next 0.1 s in opposite direction. If the final velocity of the body is 5 ms –1 in opposite direction, the mass of the body is
Internal forces can change
A player caught a cricket ball of mass 150g moving at a rate of 20 m/s. If the catching process is completed in 0.1s, the average force of the blow exerted by the ball on the hand of the player is equal to :
A body is projected vertically upwards. Its momentum is gradually decreasing. In this
A ball falls towards the earth. Which of the following is correct?
A hammer of mass 1 kg strikes on the head of a nail with a velocity of 2 ms –1 . It drives the nail 0.01 m into a wooden block. Find the force applied by the hammer and the time of impact.
If an elevator is moving vertically upwards with an acceleration a, the force exerted on the floor by a passenger of mass M is
A lift is going up with uniform velocity. When brakes are applied, it slows down. A person in that lift, experiences
The linear momentum of a particle as a function of time t is given by p = a + bt, where a and b are positive constants. The force acting on the particle is
An impulse “I” given to a body changes its velocity from “v 1 to v 2 “. The increase in the kinetic energy of the body is given by
The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time inerval from zero to 8 s is
A force-time graph for the motion of a body is shown in figure. Change in linear momentum between 0 and 8 s, is
A body of mass m is projected at an angle θ to the horizontal, the projectile at the highest point breaks into two fragments of equal masses. One of the fragments retraces its path to the point of projection. The velocity of the other fragment just after explosion is
A particle of mass 1 kg is thrown vertically upward with speed 100 m/s. After 5 sec it explodes into two parts. One part of mass 400 g comes back with speed 25 m/s, what is the speed of the other part just after explosion? (g=10 m/s 2 )
A shell of mass 0.01 kg fired by a gun of mass 10 kg. If the muzzle speed of the shell is 50 ms –1 , what is the recoil speed of the gun?
A rocket consumes 20 kg fuel per second. The exhaust gases escape at a speed of 1000 ms –1 relative to the rocket. Calculate the upthrust received by the rocket. Also calculate the velocity acquired. When its mass is 1/100 of the initial mass.
A rocket of initial mass 6000kg ejects mass at constant rate of 200 kg/sec. with constant relative speed of 800 m/sec. The acceleration of the rocket after 5 sec is (neglect gravity)
In the given arrangement, for the system to remain under equilibrium, the ‘ θ ‘ should be
A block of mass 10 kg lying on a smooth horizontal surface is being pulled by means of a rope of mass 2 kg. If a force of 36N is applied at the end of the rope, the tension at the mid point of the rope is,
Two bodies of masses 1 kg and 2 kg are connected by a very light string passed over a clamped light smooth pulley. If the system is released from rest, find the acceleration of the two masses and the tension in the string
A block of mass 3 kg which is on a smooth inclined plane making an angle of 30 o to the horizontal is connected by a cord passing over a light frictionless pulley to a second block of mass 2 kg hanging vertically. What is the acceleration of each block and what is the tension of the cord?
Two blocks of masses 2 kg and 4 kg are connected by a light string passing over a light smooth pulley clamped to the edge of a horizontal table. The 2 kg block is on the smooth horizontal table and the other block is hanging vertically. (i) Find the acceleration of the system if it is released from rest. (ii) Find the tension in the string.
A constant force F = m 2 g/2 is applied on the block of mass m 1 as shown. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of m 1 .
Two blocks of mass 4 kg and 2 kg are connected by a heavy string and placed on rough horizontal plane. The 2 kg block is pulled with a constant force F. The coefficient of friction between the blocks and the ground is 0.5. What is the value of F so that tension in the string is constant throughout during the motion of the blocks ? (g = 10 m/s 2 )
The linear momentum of a particle varies with time t as P = a + bt + ct 2 . Then which of the following is correct ?
An object flying in air with velocity suddenly breaks in two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity . The velocity of the larger piece will be :
Statement A : Action and reaction act on two different bodies Statement B : Action, reaction never cancel each other
A person of mass m is on the floor of a lift.The lift is moving down with an acceleration ‘a’. Then : a) the net force is acting in downward direction and is equal to mg b) the force mg must be greater than reaction force c) the man appears to be lighter than his true weight by a factor (a/g)
Statement A : Shock absorbers reduce the magnitude of change in momentum. Statement B : Shock absorbers increase the time of action of impulsive force
A ball of mass 400 gm is dropped from a height of 5m. A boy on the ground hits the ball vertically upwards with a bat with an average force of 100N so that it attains a vertical height of 20m. Find the time for which the ball remains in contact with the bat
A batsman deflects a ball by an angle of 60 0 without changing its initial speed of 20 ms –1 . what is the impulse imparted to the ball if its mass is 0.15 kg?
Identify the correct order in which the value of normal reaction increases, (object is placed on rough horizontal surface) i) The object is pushed with the force F at an angle ‘θ’ with horizontal ii) The object is pulled with the force F at an angle ‘θ’ with horizontal iii) The object is pushed down with the force F normally iv) The object pulled up with the force F normally
The momentum of a body in two perpendicular direction at any time ‘t’ are given by P x = 2t 2 + 6 and . The force acting on the body at t = 2 sec is
A bullet is fired from a gun. The force on the bullet is given by F = 600 – (2 × 10 5 t), where F is in newton and ‘t’ is in second. The force on the bullet becomes zero as soon as it leaves the barrel. The average impulse imparted to the bullet is
A U – shaped smooth wire has a semicircular bending between A and B as shown in the figure. A bead of mass m moving with uniform speed v through the wire enters the semicircular bend at A and leaves at B. the average force, exerted by the bead on the part AB of the wire is
In figure shown, both blocks are released from rest. The time to cross each other is
If masses are released from the position shown in figure then time elapsed before mass m 1 collides with the floor will be :
In the figure shown block B moves down with a velocity 10 m/s. The velocity of A in the position shown is
In order to raise a mass of 100 kg a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 5g/4 relative to rope. The tension in the rope is (g = 10 m/s 2 ).
There are four forces acting at a point P produced by strings as shown in figure, which is at rest. The forces F 1 , and F 2 respectively.
If ‘O’ is at equilibrium then the values of the tension T 1 and T 2 respectively.
A person of mass 60 kg stands on a weighing machine in a lift which is moving a) upwards with a uniform retardation of 2.8 ms –2 b) downwards with a uniform retardation of 2.2 ms –2 . Find the reading shown by the weighing machine in each case.
If the ring shown in the figure is restricted to move along the rod with speed 4m/s, the velocity of the mass ‘m’ is ………. m/s
A uniform rope of mass m hangs freely from a ceiling. A bird of mass M climbs up the rope with an acceleration a. The force exerted by the rope on the ceiling is
In the figure shown, all the surfaces are smooth and the pulley is massless. A constant force of magnitude F= mg/2 is acting on the block of mass M. The acceleration of the block M is
Two blocks of masses ‘3m’ and ‘2m’ are in contact on a smooth table. A force P is first applied horizontally on block of mass ‘3m’ and then on mass ‘2m’. The contact forces between the two blocks in the two cases are in the ratio
A block of mass m is supported by a cord C from the ceiling and another cord D is attached to the bottom of the block (see figure). If D is pulled on steadily
If 4 kg block is held after 2 s of start then how high 2 kg block will rise from the beginning before coming to rest momentarily?
A homogeneous rod of length ‘L’ is acted upon by two forces F 1 and F 2 applied to its ends and directed opposite to each other. If F 2 > F 1 , then with what force ‘F’ will the rod be stretched at the cross-section at a distance l from the end where F 1 is applied
A man of mass 60 kg is standing on a massless plank and holding a string passing over a system of ideal pulleys. A mass of 20 kg hanging over a light pulley such that the system is in equilibrium. The force exerted by the plank on the man is (g=acceleration due to gravity).
In the figure the blocks A, B and C of mass m each, have acceleration a 1 , a 2 and a 3 respectively. F 1 and F 2 are external forces of magnitudes 2 mg and mg respectively.
Two masses 5 kg and 3 kg are suspended from the ends of an unstretchable light string passing over a frictionless pulley. When the masses are released, the thrust on the pulley is (g = 10ms –2 )
The reading in the spring balance is
In the given figure a block of mass 2 kg is placed on a block of mass 3 kg and the two constant forces are applied at the two ends of strings. If all the surfaces are smooth and strings and pulley are ideal then acceleration of 3 kg block is
In the balance machine shown in the figure, which arm will move downward after the system is released (assuming string and the pulley to be ideal)
In the figure, a man of true mass M is standing on a weighing machine placed in a cabin. The cabin is joined by a string with a body of mass m. Assuming no friction, and negligible mass of cabin and weighing machine, the reading of weighing machine is
In the arrangement shown in the figure, the acceleration of the pulley is, (Ignore friction and mass of the pulley).
Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force F is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force F is
A solid sphere of mass 2kg is resting inside a cube as shown in the figure. The cube is moving with a velocity Here t is time in seconds. All surfaces are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube?
A block of mass m, lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q, inclined at an angle θ to vertical. The block will remain in equilibrium, if coefficient of friction between it and surface is
A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed downward as in figure and whose equation is x 2 = ay. If the coefficient of friction is µ , the highest distance above the x-axis at which the particle will be in equilibrium is
A 60 kg box sledge is travelling horizontally on ice at a speed of 10 m s – 1 . A 90 kg packet is dropped on it vertically. The subsequent velocity of the sledge is
A shell is fired from a cannon with velocity v m/s at an angle θ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in m/s of the other piece immediately after the explosion is:
A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Take g = 10 ms – 2 )
A shell of mass 200 g is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 ms – 1 , then the recoil speed of the gun is
Match Column I with Column II and mark the correct choice from the given codes. Column-I Column-II (A) Definition of force (p) Newton’s third law (B) Measure of froce (q) Impulse (C) Effect of force r) Newton’s second law (D) Recoiling of gun (s) Newton’s first law codes
A body of mass M at rest explodes into three pieces, two of which of mass M 4 each are thrown off in perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with a velocity of
A body under the action of force F = 6 i ^ – 8 j ^ N acquires an acceleration of 5 ms – 2 .The mass of the body is
A nuclide at rest emits an α -particle. In this process:
A ball of mass m falls vertically to the ground from a height h 1 and rebound to a height h 2 . The change in momentum of the ball on striking the ground is
A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see figure). If a sudden jerk is given to C, then
A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see figure). If the string C is stretched slowly, then
Three forces starts acting simultaneously on a particle moving with velocity v . These forces are represented in magnitude and direction by the three sides of a triangle ABC(as shown). The particle will now move with velocity
A lift is going up. The total mass of the lift and the passenger is 1500 kg. The variation in the speed of the lift is as given in the graph. The tension in the rope pulling the lift at t = 11th see will be
Three particles A,B and C of equal masses move with equal speeds v along the medians of an equilateral triangle. They collide at the centroid O of the triangle. After collision A comes to rest while B retraces its path with speed v. The velocity of C is then
Figure shows the position-time (x-t) graph of one dimensional motion of a body of mass 500 g. What is the time interval between two consecutive impulses received by the body?
In the figure given below, the position – time graph of a particle of mass 0.1 kg is shown. The impulse at t = 2 sec is
A force-time graph for the motion of a body is shown in the figure. The change in the momentum of the body between zero and 10 sec is
A 2 kg toy car can move along an x axis. Graph shows force F x , acting on the car which begins at rest at time t = 0. The velocity of the particle at t = 10 s is:
The 4 kg block is suspended by two strings OA and OB as shown in figure. Then tension in the string OB is
A body at rest explodes in to two fragments ratio of whose masses is 1 : 4. If kinetic energy of the lighter mass is 12 Joule, what is the kinetic energy of the heavier mass?
A rocket of mass 50 kg is fired vertically on the surface of earth. If velocity of exhaust gases relative to the rocket is 200 m/s and fuel is consumed at the rate of 4 kg/s, acceleration of the rocket is
A thin wire is bent into the shape of a parabola in the vertical plane as shown. A small bead ‘P’ can freely slide along the wire. The coefficient of friction between the bead and the wire is ‘ μ ‘ . The condition on y so that the bead does not slip on the wire is :
In the pulley arrangement shown, the pulley P 2 is movable. Assuming coefficient of friction between m and surface to be μ , the minimum value of M for which m is at rest is
When a belt moves horizontally at a constant speed of 1.5 m/s, gravel is falling on it at 5kg/s, then the extra power needed to drive the belt is :
Two blocks of masses M 1 and M 2 , are connected with a string passing over a pulley as shown in figure. The block M 1 lies on a horizontal surface. The coefficient of friction between the block M 1 and the horizontal surface is μ . The system accelerates. What additional mass m should be placed on the block M 1 so that the system does not accelerate?
A man is raising himself and the crate on which he stands with an acceleration of 5 m / s 2 by a massless rope-and pulley arrangement. Mass of the man is 100 kg and that of the crate is 50 kg. If g = 10 m / s 2 , the contact force between man and the crate is
A mass of 4 kg is suspended by a rope of length 4 m from a ceiling. A force of 20 N in the horizontal direction is applied at the mid-point of the rope as shown in figure. What is the angle which the rope makes with the vertical in equilibrium? Neglect the mass of the rope. Take g = l0 ms – 2
A light string of 70 cm has its two ends tied at the same level 50 cm apart. A force of 100 N is applied at a distance of 30 cm from P. The tension in part PR is
Three blocks of masses m 1 , m 2 and m 3 are connected by mass less unstretchable strings on a smooth surface. Tension T 2 , is
Two masses are connected by a string which passes over a pulley accelerating upward at a rate A shown. If a 1 and a 2 be the accelerations of bodies I and 2 respectively then,
In the diagram 100 kg block is moving up with constant velocity, then find out the tension at point P
Beads A and B each of mass m, are connected by a light inextensible cord. They are constrained (restricted) to move on a frictionless ring in a vertical plane as shown. The beads are released from rest at the position shown. The tension in the cord just after the release is
A heavy particle slides under gravity down the inside of a smooth vertical tube held in vertical plane. It starts from the highest point with velocity 2 a g , where a is the radius of the circle. The angular position θ (as shown in figure) at which the vertical acceleration of the particle is maximum, is given by cos – 1 p q . Find the value of p + q .
A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it
Figures I, II, III and IV depict variation of force with time. Select the figure(s) that depicts minimum impulse delivered.
A rigid ball of mass m strikes a rigid wall at 60 o and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be
In the given figure, a = 15 m / s 2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R=2.5 m at a given instant of time. The speed of the particle is
The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is
A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1 . 0 m / s 2 . If g = 10 m / s 2 , the tension in the supporting cable is
A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the Player is
Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in figure. The system is released from rest. The larger mass is stopped 1.0 second after the system is set into motion and then released immediately. The time elapsed before the string is tight again is: Take g = 10 m / s 2
Two blocks A and B of masses 2m and m, respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring with the block A above block B . The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:
ln the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of block ‘C’ will be
In the system shown in figure m B = 4kg, and m A = 2 kg. The pulleys are massless and friction is absent everyrwhere. The acceleration of block A is
The acceleration of the blocks (A) and (B) respectively in situation shown in the flgure is: (pulleys and strings are massless)
Two blocks of masses m 1 and m 2 are connected as shown in the figure. The acceleration of the block m 2 , is:
ln the figure shown neglecting friction and mass of pulleys, what is the acceleration of mass B?
In the figure acceleration of A is 1 m / s 2 upwards, acceleration of B is 7 m / s 2 upwards and acceleration of C is 2 m / s 2 upwards. The acceleration of D will be
For the pulley system shown, each of the cables at A and B is given a velocity of 2 m/s in the direction of the arrow. Determine the upward velocity v of the load m.
If the blocks are moving as shown in the figure the relation between a 1 , a 2 and a 3 will be
ln each of the three arrangements, the block of mass m 1 is being pulled left with constant velocity. There is no friction any where. The strings are light and inextensible and pulleys are massless. The ratio of the speed of the block of mass m 2 in three cases respectively is:
In the arrangement shown, the pulleys and the strings are ideal. The acceleration of block B is
Find velocity of ring B ( V B ) at the instant shown. The string is taut and inextensible:
Three blocks l, 2 and 3 are arranged as shown in the figure. The velocities of the blocks v 1 , v 2 and v 3 are shown in the figure. What is the relationship befween v 1 , v 2 and v 3 ?
A large cubical shaped block of mass M rests on a fixed horizontal surface. Two blocks of mass m 1 aod m 2 are connected by a light inextensible string passing over a light pulley as shown. Neglect friction everyvhere. Then the constant horizontal force of magnitude F that should be applied to M so that m 1 and m 2 do not move relative to M is:
A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration ‘a’ directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration ‘a'(relative to car) vertically. The tension in the string is equal to
A block is kept on a frictionless inclined surface with angle of inclination ‘ α ‘. The incline is given an acceleration ‘a’ to keep the block stationary. Then a is equal to
Consider the system as shown in the figure. The pulley and the string are light and all the surfaces are frictionless. The tension in the string is (g: l0 m / s 2 )
In the given diagram, with what force must the man pull the rope to hold the plank in position? Mass of the man is 80 kg. Neglect the weights of plank, rope and pulley. Take g= l0 ms – 2 .
Consider the three cases given in figures shown. Assume the friction to be absent everywhere and the pulleys to be light; the string connecting the blocks to other block or flxed vertical wall to be light and inextensible . Let T A , T B and T C be the tension in the strings in figure A, figure B and figure C respectively. Then pick the correct comparison between the given tensions (for the instant shown) from options below.
Two masses m and M are attached with strings as shown. For the system to be in equilibrium we have
A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by
There are four forces acting at a point P produced by strings as shown in figure, which is at rest. The forces F 1 and F 2 rare
A weight W is supported by two strings inclined at 60° and 30° to the vertical. The tensions in the strings are T 1 and T 2 , as shown. If these tensions are to be determined in terms of W using a triangle of forces, which of these triangles should you draw? (block is in equilibrium)
ln the figure shown ‘P’ is a plate on which a wedge B is placed and on B a block A of mass m is placed. The plate is suddenly removed and system of B and A is allowed to fall under gravity. Neglecting any force due to air on A and B, the normal force on A due to B is
A body of mass 2.0 kg is placed on a smooth horizontal surface. Two forces F 1 = 20 N and F 2 = 10 3 N are acting on the body in directions making angles of 30° and 60° to the surface. The reaction of the surface on the body will be
A block of mass 3 kg is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be
A 15 kg block is initially moving along a smooth horizontal surface with a speed of v = 4 m/s to the left. It is acted by a force F, which varies in the manner shown. Determine the velocity of the block at t = 15 seconds. Given that, F = 40 cos ( π 10 ) t .
A 100 g iron ball having velocity l0 m/s collides with a wall at an angle 30° and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the wall is
Two bodies of mass 4 kg and 6 kg are attached to the ends of a string passing over a pulley. The 4 kg mass is attached to the table top by another string. The tension in this string T 1 , is equal to: Take g = l0 m / s 2
Three identical rigid circular cylinders A, B and C are arranged on smooth inclined surfaces as shown in figure. The least value of θ that prevent the arrangement from collapse is
Two smooth spheres each of radius 5 cm and weight W rest one on the other inside a fixed smooth cylinder of radius 8 cm. The reactions between the spheres and the vertical side of the cylinder are:
In the following figure, the pulley P 1 is fixed and the pulley P 2 is movable. lf W 1 = W 2 = 100 N, what is the angle A P 2 P 1 ? The pulleys are frictionless.
A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of the following statements is NOT correct?
A particle of mass ‘m’ and initially at rest is acted by a force F = a t. N . Best representation of force displacement graph is (S assumes positive values only ) :
A bomb of mass 9 kg explodes into 2 pieces of mass 3 kg and 6 kg. The velocity of mass 3 kg is 1.6 m/s. The K.E. of mass 6 kg is
Two masses m 1 = 1 kg and m 2 = 2 kg arc connected by a light inextensible string and suspended by means of a weightless pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in two seconds is (Take g = 10 ms – 2 )
A block of mass 4kg is pressed against a wall by two perpendicular horizontal forces as shown in the figure. F 1 is perpendicular to the wall and F 2 is parallel to the wall. μ s = 0.8 , μ k = 0.5 and g = 10 m / s 2 For F 1 = 75 N and F 2 = 30 N , the block remains at rest on the wall then the force of friction is
In the figure shown if mass of each block is m. Find the acceleration of block A. (use g=10 m/s 2 )
In the arrangement shown, the blocks are connected by a light string and they are placed on a frictionless horizontal surface. If the 4 kg block is pulled to the right by a force F, tension in the string is found to be 20 N. If the 2 kg block is pulled to the left by the same force F, tension in the string will be
Two blocks are connected by a spring. The combination is suspended, at rest, from a string attached to the ceiling, as shown in the figure. The string breaks suddenly. Immediately after the string breaks, if the initial acceleration of the upper block is found to be ng/2. The value of n is
Three identical rigid circular cylinders A, B and C are placed on smooth inclined plane shown in the figure. The minimum value of tan θ that prevent the arrangement from collapse is 1 3 n . The value of n is
A block of mass m is connected to a peg at point D through a light and inextensible string of length 18 m. The length of section AB is 3 m. The point C of string is pulled down by applying a force F of 128 N. Block A remains stationary. If the mass of block A is 16 n kg, the value of n is
For the situation shown in the figure, pulleys are light and smooth. Pulleys C and D are fixed, but A and B are movable. Find the value of m (in kg) if m is in equilibrium. (take, m 1 = 2 kg and m 2 =1 kg)
A block B of mass 1 kg is placed on a light plank shown in figure. A force F of 10 N is applied on the plank horizontally. Find the acceleration (in m/s 2 ) of block B.
Two blocks of masses 25 kg and 5 kg are placed on a horizontal table as shown in figure. A massless string passes over a frictionless and massless pulley whose one end is connected to 25 kg block and the other end is connected to block M. The coefficient of friction between two blocks is μ =0.3 and between the 5 kg block and ground is zero. The system is released from rest. If M = 45 kg the force of friction between two blocks (in N) is (Take g = 10 m/s 2 )
A 10 kg boy standing in a 40 kg boat floating on water is 20 m away from the shore of the river. If the boy moves 8 m on the boat towards the shore, then how far is he from the shore? (Assume no friction between boat and water)
A boy of mass m is standing on a block of mass M kept on a rough surface. When the boy walks from left to right on the block, the centre of mass (boy + block) of system:
Consider a large block placed on a smooth horizontal surface, with a man standing at one end of the block. The man walks to the other end, relative to the block. The distances (absolute) moved by the man and the block are:
A trolley containing water has total mass 1000 kg. Now water starts coming out of the trolley at the rate of 10 kg/s from below it. Find the velocity of the trolley after 50 sec, if the initial speed is 10 m/s on the horizontal frictionless road.
Two springs of spring constants k 1 and k 2 are joined in series. The effective spring constant of the-combination is given by:
A block of metal weighing 2 kg is resting on a frictionless plane. It is struck by a jet releasing water at a rate of 1 kg/s and at a speed of 5 m/s. The initial acceleration of the block will be:
Three equal weights of mass 2 kg each are hanging on a string passing over a fixed pulley as shown in Figure. What is the tension in the string connecting weights B and C ?
Two blocks of masses 2 kg and I kg are in contact with each other on a frictionless table. When a horizontal force of 3.0 N is applied to the block of mass 2 kg, the value of the force of contact between the. two blocks is:
Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 15 kg weight is attached to the rope at the mid point which now no longer remains horizontal. The minimum tension required to completely straighten the rope is:
A boy of mass 40 kg is hanging from the horizontal branch of a tree. The tension in his arms is minimum when the angle between the arms is:
A chain of mass M and length I is held vertical by fixing its upper end to a rigid support. The tension in the chain at a distance y from the rigid support is:
Find the tension T 2 in the system shown in Figure
A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its ends. Tension in the string at a distance x from the end at which force is applied is:
Three blocks are connected as shown in the Figure on a horizontal frictionless table. If m 1 = 1 kg, m 2 = 8 kg, m 3 : 27 kg and T 3 = 36 N, T 2 will be:
An elevator starts from rest with a constant upward acceleration. It moves 2 m in the first 0.6 second. A passenger in the elevator is holding a 3 kg package by a vertical string. When the elevator is moving, what is the tension in the string?
In the Figure given below two masses m and m’ are tied with a thread passing over a pulley, m’ is on a frictionless horizontal surface. If acceleration due to gravity is g, the acceleration of m’ in this arrangement will be:
In the system shown in Figure, the pulley is frictionless and the string massless. If m 1 = m 2 , thrust on the pulley will be:
A person wishes to slide down a rope whose breaking load is 3 5 of the weight of the person. Minimum acceleration by which the person should slide down without breaking the rope is:
Two masses m 1 and m 2 are connected to the ends of a massless string that passes over a pulley fixed at the top of a double incline as shown. Assuming m 1 > m 2 , acceleration of the system is:
A block of mass ‘m’ is placed on a frictionless inclined plane of inclination θ with horizontal. The inclined plane is accelerated horizontally so that the block does not slide down. In this situation, vertical force exerted by the inclined plane on the block is:
An open knife edge of mass M is dropped from a height ‘h’ on a wooden floor. If the blade penetrates a distance ‘S’ into the wood, average resistance offered by the wood to the blade is:
A train having 60 compartments is pulled by engine with a force 6 x 10 4 N. If mass of each compartment is 4000 kg, the tension in the coupling between 40th and 41st compartment is:
A monkey of mass 30 kg climbs a rope which can withstand a maximum tension of 360 N. The maximum acceleration which this rope can tolerate for the climbing of monkey is: (g = 10 m/s 2 )
P, Q and R are three coplanar forces acting at a point and are in equilibrium. Given P=1.9318 kg wt., sin θ 1 = 0.9659 , the value of R is ( in kg wt.)
An object of m kg with speed of v m/s strikes a wall at an angle θ and rebounds at the same speed and same angle. The magnitude of the change in momentum of the object will be
A particle moves so that its position vector varies with time as r = A cos ω t i ^ + A sin ω t j ^ . The initial velocity of the particle is
A string of negligible mass going over a clamped pulley of mass m supports a block of mas s M as shown in the Figure . The force on the pulley by the clamp is given by:
The pulleys and strings shown in the Figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be:
A bullet of mass 0.05 kg moving with a speed of 80 m/s enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the bullet is:
The velocity of a body of mass 20 kg decreases from 20 m/s to 5 m/s in a distance of 100 m. Force on the body is:
Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force F = 10 N, then tension T 1 is :
A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s 2
A small ball is suspended from a thread. It is lifted up with an acceleration 4.9 m/s 2 and lowered with an acceleration 4.9 m/s 2 , then the ratio of tensions in the thread in both cases will be :
For a rocket propulsion velocity of exhaust gases relative to rocket is 2 km/s. If mass of rocket system is 1000 kg, then the rate of fuel consumption for a rocket to rise up with acceleration 4.9 m/s 2 will be :
In shown figure m 1 = 2kg and m 2 – 4 kg. The pulley is movable. At t = 0, both masses touch the ground and the string is taut. A vertically upward force F = 2t (F is in newton and t is in second) is applied to the pulley” the time when m 2 is lifted off the ground is:
A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1.0 m/s 2 . If g = 10ms -2 , the tension in the supporting cable is :
When forces F 1 , F 2 , F 3 are acting on a particle of mass m such that F 2 and F 3 are mutually perpendicular, then the particle remains stationary. If the force F 1 is now removed then the acceleration of the particle is :
A body of mass 10 kg is acted upon by two perpendicular forces 6 N and 8 N. The resultant acceleration of the body is : (i) 1ms -2 at an angle of tan − 1 4 3 w.r.t. 6 N force (ii) 0.2ms -2 at an angle of tan − 1 4 3 w.r.t. 6 N force (iii) 1ms -2 at an angle of tan − 1 3 4 w.r.t. 8N force (iv) 0.2ms -2 at an angle of tan − 1 3 4 w.r.t. 8N force
A body of mass 2kg travels according to the law x(t) = pt + qt 2 + rt 3 where p = 3ms -1 , q = 4ms -2 and r = 5ms -3 . The force acting on the body at t = 2 seconds is :
A man weighs 80 kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 m/s 2 . What would be the reading on the scale ? (g = 10 m/s 2 )
Three blocks with masses m,2m and 3m are connected by strings, as shown in Figure . After an upward force F is applied on block m, the masses move upward at constant speed v What is the net force on the block of mass 2m? (g is the acceleration due to gravity)
A balloon with mass ‘m’ is descending down with an acceleration ‘a’ (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration ‘a’ ?
A rocket having initial mass of 1000 kg burns fuel at the rate of 4 kg/s. If the speed of exhaust gases relative to the rocket is 3000 m/s, the initial thrust on the rocket is:
Three blocks A,B and C of masses 4 kg, 2 kg and 1kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is :
Find tension in string if θ =30° and the mass hanged in middle of the string is equal to 22 kg.
A sphere of radius 25 cm and mass 1 kg is hung by a string of negligible mass and length 40 cm, then tension in the string is :
Force of 3N acts on a system of two blocks of mass 2 kg and 1 kg as shown in figure. Contact force between the blocks is :
In a legend the hero kicked a baby pig so that he is projected with a speed greater than that of his cry. If the weight of the baby pig is assumed to be 5 kg and the time of contact 0.01 sec, the force with which the hero kicked him was:
A machine gun fires a bullet of mass 40 gm with a speed 1200 m/s. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
A body with mass 5 kg is acted upon by a force F = ( − 3 i ^ + 4 j ^ ) N If its initial velocity at t = 0 is v = ( 6 i ^ − 12 j ^ ) ms − 1 , the time at which it will just have a velocity along the y-axis is :
A ball is thrown up at an angle with the horizontal. Then the total change of momentum by the instant it returns to ground is :
A player caught a cricket ball of mass I50 gm moving at the rate of 20 ms -1 . If the catching process be completed in 0.1 s, the force of the blow exerted by the ball on the hands of the player is :
A 0.5 kg ball moving with a speed of l2 m/s strikes a hard wall at an angle of 30° with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 seconds, the average force acting on the wall is :
Velocity of a particle of mass 2 kg varies with time ‘t’ according to the equation v = ( 2 t i ^ − 4 j ^ ) m / s m/s. Here ‘r’ is in seconds. The impulse imparted to the particle in the time interval 0 ≤ t ≤ 2s is:
The position-time graph of a body of mass 2 kg is shown in Figure. What is the impulse on the body at t = 4 s ?
Waterjet is coming out of a hose pipe of diameter 20 cm with speed 20 cm/sec. It strikes a man in elastically. Find the force exerted by water jet on the person
The force ‘F’ acting on a particle of mass ‘m’ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is:
Choose the INCORRECT statement (with respect to the 2nd law of motion)
Two identical blocks A and B each of weight 20 N are placed on a frictionless horizontal plane. The portion of the string connected to B is vertical and that connected to A makes an angle of 53° with the plane. The minimum horizontal force F required to lift the block B is :
A particle is moving in free space with some velocity as shown. It is applied by force F 1 , F 2 a n d F 3 of magnitude 10N, 10N and 15N respectively :
Three boxes are placed in a lift. When acceleration of the lift is 4 m/s 2 , the net force on the 8 kg box is closest to :
A 0.5 kg ball moving with a speed of 12 m/sec strikes a hard wall at an angle of 30 0 with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is
A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see figure). If a sudden jerk is given to C, then
A machine gun fires a bullet of mass 40 g with a velocity 1200 ms -1 . The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
A block of mass m is placed on a smooth wedge of inclination θ . The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be
In the following diagram, pulley P 1 is movable and pulley P 2 is fixed. The value of angle θ will be
A man of mass m stands on a crate of mass M. He pulls on a light rope passing over a smooth light pulley. The other end of the rope is attached to the crate. For the system to be in equilibrium, the force exerted by the men on the rope will be
The two pulley arrangements shown in the figure are identical. The mass of the rope is negligible. In (a) the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (b). m is lifted up by pulling the other end of the rope with a constant downward force of 2mg. The ratio of accelerations in two cases will be
Five forces F 1 , F 2 , F 3 , F 4 and F 5 , are acting on a particle of mass 2.0 kg so that it is moving with 4 m/s 2 in east direction. If F 1 force is removed, then the acceleration becomes 7 m/s 2 in north, then the acceleration of the block if only F 1 is acting will be
The ratio of tensions in the string connected to the block of mass m 2 in Figure (a) and Figure (b) respectively, is (friction is absent everywhere): m 1 = 50 kg , m 2 = 80 kg and F = 1000 N ]
Two small spheres each of mass m connected by a string of length 2l are kept on a smooth horizontal surface. A vertical force F is applied at the middle of the string. What is maximum value of F for which the spheres do not lose contact with the surface?
A block of mass 2kgslides down the face of a smooth 45 o wedge of mass 9 kg as shown in the figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge.
Two identical small masses each of mass m are connected by a light inextensible string on a smooth horizontal floor. A constant force F is applied at the mid point of the string as shown in the figure. The acceleration of each mass towards each other is,
Three forces are acting on a particle of mass m initially in equilibrium. If the first two forces (R 1 and R 2 ) are perpendicular to each other and suddenly the third force (R 3 ) is removed, then the acceleration of the particle is
A ball of mas s m moving with a velocity u rebounds from a wall. The collision is assumed to be elastic and the force of interaction between the ball and wall varies as shown in the figure. Then the value of F 0 is
n balls each of mass m impinge elastically each second on a surface with velocity u. The average force experienced by the surface will be
A rope is stretched between two boats at rest. A sailor in the first boat pulls the rope with a constant force of 100 N. First boat with the sailor has a mass of 250 kg where as the mass of second boat is double of this mass. If the initial distance between the boats was 120 m, the time taken for two boats to meet each other is (neglect water resistance between boats and water)
A particle of mass 2 kg moves with an initial velocity of v = 4 i ^ + 4 j ^ ms − 1 . A constant force of F = – 20 j ^ N is applied on the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle when its y-coordinate again becomes zero is given by
A block of metal weighing 2kgis resting on a frictionless plane. It is struck by a jet releasing water at a rate of 1 kgs -1 and at a speed of 5 ms -1 . The initial acceleration of the block is
Figure shows the variation of force acting on a body with time. Assuming the body to start from rest, the variation of its momentum with time is best represented by which plot?
A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500 m/sec with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is
A particle is moving in the x-y plane. At certain instant of time, the components of its velocity and acceleration are as follows: v x = 3 ms − 1 , v y = 4 ms − 1 , a x = 2 ms − 2 and a y = 1 ms − 2 . The rate of change of speed at this moment is
Five persons A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration 3 m/s 2 in east direction. When person A stops pulling, it moves with acceleration 1 m/s 2 in the west direction. When person B stops pulling, it moves with acceleration 24 m/s 2 in the north direction. The magnitude of acceleration of the cart when only A and B pull the cart keeping their directions same as the old directions, is
In order to raise a mass of 100 kg, a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with acceleration 5g/4 relative to the rope. The tension in the rope is (take g=10 ms -2 )
A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination 30 o with horizontal. The acceleration of train up the plane is a = g/2. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is
A balloon of mass M is descending at a constant acceleration a. When a mass m is released from the balloon, it starts rising with the same acceleration a. Assuming that its volume does not change, what is the value of m?
A trolley T of mass 5 kg on a horizontal smooth surface is pulled by a load of 2 kg through a uniform rope ABC of length 2 m and mass 1 kg. As the load falls from BC = 0 to BC = 2 m, its acceleration (in ms -2 ) changes from
Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to the block of mass M as shown in the figure. The magnitude of force P is
A man is raising himself and the crate on which he stands with an acceleration of 5 ms -2 by a massless rope-and-pulley arrangement. Mass of the man is 100 kg and that of the crate is 50 kg. If g=10 ms -2 , then the tension in the rope is
In the figure, the mass m 2 starts with velocity v 0 and moves with constant velocity on the surface. During motion, the normal reaction between the horizontal surface and fixed triangle block m 1 is N. Then during motion
Two objects A and B, each of mass m, are connected by a light inextensible string. They are restricted to move on a frictionless ring of radius R in a vertical plane (as shown in the figure). The objects are released from rest at the position shown. Then the tension in the cord just after release is
A lift is moving down with an acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift, and a man standing stationary on the ground are, respectively,
Block B has mass m and is released from rest when it is on top of wedge A, which has a mass 3m. Determine the tension in cord CD needed to hold the wedge from moving while B is sliding down A. Neglect friction.
An object is suspended from a spring balance in a lift. The reading is 240N when the lift is at rest. If the spring balance reading now changes to 220 N, then the lift is moving
As shown in the figure, if acceleration of M with respect to ground is 2 ms- 2 , then
A painter of mass M stands on a platform of mass m and pulls himself up by two ropes which hang over pulley as shown in the figure. He pulls each rope with force F and moves upward with a uniform acceleration a. Find a, neglecting the fact that no one could do this for long time.
A man pulls himself up the 30 o incline by the method shown in the figure. If the combined mass of the man and cart is 100 kg, determine the acceleration of the cart if the man exerts a pull of 250 N on the rope. Neglect all friction and the mass of the rope, pulleys, and wheels.
A 60-kg man stands on a spring scale in a lift. At some instant, he finds that the scale reading has changed from 60 kg to 50 kg for a while and then comes back to original mark. What should be concluded?
Figure represents a light inextensible string ABCDE in which AB = BC = CD = DE and to which are attached masses M, m, and M at the points B, C, and D, respectively. The system hangs freely in equilibrium with ends A and E of the string fixed in the same horizontal line. It is given that tan α = 3/4 and tan β = 12/5. Then the tension in the string BC is
Two particles A and B , each of mass m, are kept stationary by applying a horizontal force F = mg on particle B as shown in the figure. Then
A block A has a velocity of 0.6 ms -1 to the right. Determine the velocity of cylinder B.
In the figure, a person wants to raise a block lying on the ground to a height h. In both the cases, if the time required is same, then in which case he has to exert more force? Assume pulleys and strings light.
In the following arrangement, the system is initially at rest. The 5-kg block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of block C will be
In the figure, blocks A and B move with velocities v 1 and v 2 along horizontal direction. Find the ratio of v 1 /v 2 .
If block B moves towards right with acceleration b, find he net acceleration of block A.
If the blocks A and B are moving towards each other with accelerations a and b as shown in the figure, find the net acceleration of block C.
In the arrangement shown in the figure, if the acceleration of B is a , then find the acceleration of A.
If the acceleration of wedge in the shown arrangement is a ms -2 towards left, then at this instant, acceleration of the block (magnitude only) would be
In the arrangement shown in the figure at a particular instant, the roller is coming down with a speed of 12 m s -1 and C is moving up with 4 ms -1 . At the same instant, it is also known that w.r.t. pulley P, blockr4 is moving down with speed 3 ms -1 . Determine the motion of block B (velocity) w.r.t. ground.
Figure shows two blocks, each of mass m. The system is released from rest. If accelerations of blocks A and B at any instant (not initially) are a 1 and a 2 , respectively, then .
In the figure acceleration of A is 1 m/s 2 upwards, acceleration of B is 7 m/s 2 upwards and acceleration of C is 2 m/s 2 upwards. The acceleration of D will be
A bead of mass m is attached to one end of a spring of natural length R and spring constant k = ( 3 + 1 ) m g R . The other end of the spring is fixed at a point A on a smooth vertical ring of radius R as shown in the figure. The normal reaction at B just after it is released to move is
The system shown in the figure is released from rest. The spring gets elongated (Neglect the friction and masses of pulley, string, and spring.)
In the situation as shown in figure if acceleration of B is a then find the acceleration of A (B always remains horizontal)
The tension in the spring is
For the system shown in the figure, m 1 > m 2 > m 3 > m 4 . Initially, the system is at rest in equilibrium condition. If the string joining m 4 and ground is cut, then just after the string is cut. Statement I: m 1 , m 2 , m 3 remain stationary. Statement II: The value of acceleration of all the four blocks can be determined. Statement III: Only m 4 remains stationary. Statement IV: Only m 4 accelerates. Now, choose the correct options.
A block of mass 10 kg is suspended through two light spring balances as shown in figure.
Two blocks A and B of masses 2 m and m, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
Initially the spring is undeformed. Now the force F is applied to B as shown in the figure. When the displacement of B w.r.t. A is x towards right in some time then the relative acceleration of B w.r.t. A at that moment is
Two blocks of mass 2 kg are connected by a massless ideal spring of spring constant k = 10 N/m. The upper block is suspended from roof by a light string A. The system shown is in equilibrium. The string A is now cut, the acceleration of upper block just after the string A is cut will be g = 10 m / s 2
A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown in figure. One end of the rope is held by Student A of mass 70 kg, who is at rest on the floor. The opposite end of the rope is held by Student B of mass 60 kg, who is suspended at rest above the floor. The minimum acceleration a 0 with which the Student B should climb up the rope to lift the Student A upward off the floor.
A bullet of mass m moving with velocity v 0 hits a wooden plank A of mass M placed on a smooth horizontal surface. The length of the plank is ℓ . The bullet experiences a constant resistive force F inside the block. The minimum value of v 0 such that it is able to come out of the plank is
A wedge of mass m is pushed with a speed v 0 on a rough horizontal plane. The angle of friction between the wedge and horizontal plane is ϕ . The angle of inclination θ of the pendulum is
A block of mass m lies on wedge of mass M, which lies on fixed horizontal surface. The wedge is free to move on the horizontal surface. A horizontal force of magnitude F is applied on block as shown, neglecting friction at all surfaces, the value of force F such that block has no relative motion w.r.t. wedge will be: (where g is acceleration due to gravity)
A particle of mass m is placed on the smooth face of an inclined plane of mas s M and slope θ which is free to slide on a smooth horizontal plane in a direction perpendicular to the edge. If the particle slides with an acceleration a, the acceleration of the inclined plane towards right A will be
In the arrangement shown in the figure pulleys A and B are massless and the thread is inextensible. Mass of pulley C is equal to m. If friction in all the pulleys is negligible, then
The system starts from rest and A attains a velocity of 5 m/s after it has moved 5 m towards right. Assuming the arrangement to be frictionless everywhere and pulley and strings to be light, the value of the constant force F applied on A is
In the figure shown C is a fixed wedge on horizontal surface. Blocks A and B are of masses m and 2 m respectively are kept as shown in figure. They can slide along the inclined plane smoothly. The pulley and string are massless. Take θ =30 o and g = 10 m/s 2 . The inclined planes are very Long. A and B are released from rest. 2 seconds after the release, B is caught for a moment and released again. Find out the speed of A just before the instant when the string becomes tight again.
In the figure below, the velocities of different blocks are shown The velocity of C (in m/s) is
Figure shows a ball of mas s m connected with two ideal springs of force constant k, kept in equilibrium on a smooth incline, suddenly right spring is cut. What is magnitude of instantaneous acceleration (in m/s 2 ) of ball?
Two masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass at the instant when the 10 kg mass has an acceleration of 12 ms -2 towards right, find the acceleration of the 20kg mass in ms -2 .
Block of 3 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t = 0 then, find acceleration of block in ms -2 at t = 0.
Two blocks are arranged as shown in figure. Assuming the surfaces and the pulleys P 1 and P 2 are all smooth and pulleys and string are light, if the acceleration of the block B is found to be n F 17 m m / s 2 . The value of n is
Two blocks are connected by a spring. The combination is suspended, at rest, from a string attached to the ceiling, as shown in the figure. The string breaks suddenly. Immediately after the string breaks, if the initial acceleration of the upper block is found to be ng/2. The value of n is .
A block of mass m is connected to a peg at point D through a light and inextensible string of length 18 m. The length of section AB is 3 m. The point C of string is pulled down by applying a force F of 128 N. Block A remains stationary. If the mass of block,4 is 16 n kg, the value of n is .
Three identical rigid circular cylinders A, B and C are placed on smooth inclined plane shown in the figure. The minimum value of tan θ that prevent the arrangement from collapse is 1 3 n . The value of n is .
The situation shown in the figure, all surfaces are frictionless. Masses of blocks B and C are 1 kg and 2kg, respectively. Find the mass of the blocks A for which the block B remains stationary with respect to block C.
Reading shown in two extended spring balances, S 1 and S 2 is 60 kg and 30 kg respectively and lift is accelerating upward with acceleration 10 m/s 2 . The mass is stationary with respect to lift. Find the mass of the block in kg.
In the arrangement shown, the pulleys are smooth and the strings are inextensible. Find the acceleration of block B in m/s 2 . Take g=10 m/s 2
In the figure a block A of mass m is attached at one end of a light spring and the other end of the spring is connected to another block B of mass2m through a light string. A is held and B has obtaiwwned equilibrium. Now A is released. The acceleration of Ajust after that instant is a. The same thing is repeated for B.In that case the acceleration of B is b, then the value of a/b is .
Find the reading of spring balance (in N) as shown in figure. Assume that mass M is in equilibrium.
In the system of pulleys shown what should be the value of m 1 (in gram) such that 100 g remains at rest. (Take g = 10 m / s 2 )
In the system shown, block A is of mass 4.0 kg and blocks B and C are of equal mass each of 3 kg. Find the acceleration in m/s 2 of block C, if the system is set free. g = 10 m / s 2
A block of weight W produces an extension of 9 cm when it is hung by an elastic spring of length 60 cm and is in equilibrium. The spring is cut into two parts, one of length 40 cm and the other of length 20 cm. The same load W hangs in equilibrium supported by both parts as shown in the figure. Find the extension (in cm) in the spring.
n balls each of mass m impinge elastically in each second on a surface with velocity u. The average force experienced by the surface will be
A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle 45° with the initial vertical direction is
The displacement of a body moving along a straight line is given by : S = bt n , where ‘b’ is a constant and ‘t’ is time. For what value of ‘n’ the body moves under the action of constant force?
In the following figure, the pulley is massless and frictionless. There is no friction between the body and the floor. The acceleration produced in the body when it is displaced through a certain distance with force ‘P’ will be
Two identical blocks each of mass “M” are tied to the ends of a string and the string is laid over a smooth fixed pulley. Initially the masses are held at rest at the same level. What fraction of mass must be removed from one block and added to the other , so that it has an acceleration of 1/ 5 th of the acceleration due to gravity
A 40 N block is supported by two ropes. One rope is horizontal and the other makes an angle of 30° with the ceiling. The tension in the rope attached to the ceiling is approximately :
The pulley arrangements shown in figure are identical, the mass of the rope being negligible. In case I, the mass m is lifted by attaching a mass 2m to the other end of rope while in the second case the rope is pulled with a constant downward force F = 2mg, where g is acceleration due to gravity. The acceleration of mass m in case I is
Two masses of 10 kg and 5 kg are suspended from a rigid support as shown in figure. The system is pulled down with a force of 150 N attached to the lower mass. The string attached to the support breaks and the system accelerates downwards. In case the force continues to act. what will be the tension acting between the two masses?
Two bodies of masses 3kg and 2kg are connected by a long string and the string is made to pass over a smooth fixed pulley. Initially the bodies are held at the same level and released from rest. The velocity of the 3kg body after one second is (g=10m/ s 2 )
The velocity of a body as a function of time t is given as v = 2 t i ^ + t 2 j ^ m / s . What is force acting on the body at t = 2 s if its mass is 4 kg?
If m 1 = 10kg,m 2 = 4kg,m 3 = 2kg, the acceleration of system is
The string between blocks of masses ‘m’ and ‘2m’ is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut, the magnitudes of accelerations of masses 2m and m (immediately after cutting)
All surfaces are smooth. The acceleration of mass m relative to the wedge is
Two trolleys of masses m and 3m are connected by a spring. They are compressed and released, they move off in opposite direction and come to rest after covering distances s 1 and s 2 respectively. If the frictional force between trolley and surface is same in both the cases then the ratio of distances s 1 : s 2 is
Two particles of masses m 1 and m 2 in projectile motion have velocities v 1 and v 2 respectively at time t = 0. They collide at time t 0 . Their velocities become v 1 1 and v 2 1 at time 2t 0 while still moving in air. The value of m 1 v 1 1 + m 2 v 2 1 − m 1 v 1 + m 2 v 2 is
Two masses M 1 and M 2 connected by means of a string which is made to pass over light, smooth pulley are in equilibrium on a fixed smooth wedge as shown in figure. If θ = 60 ∘ and α = 30 ∘ ,then the ratio of M 1 to M 2 is
A 1N pendulum bob is held at an angle θ from the vertical by a 2 N horizontal force F as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is
The horizontal acceleration that should be given to a smooth inclined plane of angle sin − 1 1 l to keep an object stationary on the plane, relative to the inclined plane is
A boy of mass 50 kg is standing on a weighing machine placed on the floor of a lift. The machine reads his weight in newtons. The reading of the machine if the lift is moving upwards with uniform speed of 10 ms -1
A body of mass 3 kg is moving along a straight line with a velocity of 24ms -1 . When it is at a point ‘P’ a force of 9 N acts on the body in a direction opposite to its motion. The time after which it will be at ‘P’ again is,
A stream of water flowing horizontally with a speed of 15 ms -1 pushes out of a tube of cross sectional area 10 -2 m 2 and hits a vertical wall near by what is the force exerted on the wall by the impact of water assuming. that it does not rebound? (Density of water=1000 kg m -3 )
A base ball of mass 150 gm travelling at speed of 20 m/s is caught by a fielder and brought to rest in 0.04 s. The force applied to the ball and the distance over which this force acts are respectively
The elevator shown in figure is descending with an acceleration of 2m/s 2 . The mass of the block A = 0.5 kg. The force exerted by the block A on block B is
When a train starting from rest is uniformly accelerating, a plumb bob hanging from the roof of a compartment is found to be inclined at an angle of 45 o with the vertical . The time taken by the train to travel a distance of ½ km will be nearly
Three blocks of equal masses (each 3kg) are suspended by weightless strings as shown. If applied force is 100N,then T 1 is equal to (g =10m/ s 2 )
The pulley and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle ‘ θ ‘ should be
In the figure shown a 3 = 6m/s 2 (downwards) and a 2 = 4m/s 2 (upwards). Find acceleration of 1.
A piece of wire is bent in the shape of a parabola y = kx 2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is :
The system is pushed by a force F as shown in the figure. All surfaces are smooth except between B and C. Coefficient of friction between B and C is μ . Minimum value of F to prevent block B from downward slipping is
A body is moving down a long inclined plane of angle of inclination θ . The coefficient of friction between the body and the plane varies as μ = 0.5 x, where x is the distance moved down the plane. The body will have the maximum velocity when it has travelled a distance x given by
A boy of mass m is sliding down a vertical pole by pressing it with a horizontal force f. If μ is the coefficient of friction between his palms and the pole, the acceleration with which he slides down will be
A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in the figure. The horizontal velocity of the block is
A cylinder of mass 10 kg is sliding on a plane with an initial velocity of 10 m/s. If coefficient of friction between surface and cylinder is 0.5, then before stopping it will describe
A bomb of mass 3.0 Kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s. The total energy imparted to the two fragments is
An object of mass 3m splits into three equal fragments. Two fragments have velocities v j ^ and v i ^ . The velocity of the third fragment is
A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses 1 g and 3 g. The total K.E. of the fragments is 6 .4 × 10 4 J . What is the K.E. of the smaller fragment
A body is moving with a velocity v, breaks up into two equal parts. One of the part retraces back with velocity v. Then the velocity of the other part is
If a shell fired from a cannon, explodes in mid air, then
A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 ms -1 . The kinetic energy of the other mass is
A shell of mass m moving with velocity v suddenly breaks into 2 pieces. The part having mass m/4 remains stationary. The velocity of the other shell will be
At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two radius vectors connecting point of explosion to fragments to make 90° is
A body of mass 50 kg is projected vertically upwards with velocity of 100 m/sec. 5 seconds after this body breaks into 20 kg and 30 kg. If 20 kg piece travels upwards with 150 m/sec, then the velocity of other block will be
Conservation of momentum in a collision between particles can be understood from
A bullet of mass 50 gram is fired from a 5 kg gun with a velocity of 1km/s. the speed of recoil of the gun is
If the elevator in the shown figure is moving upwards with constant acceleration 1 ms -2 , the tension in the string connected to block A of mass 6kg would be (Take, g = 10 ms -2 )
A block is placed on the top of a smooth inclined plane of inclination θ kept on the floor of a lift. When the lift is descending with a retardation a, the block is released. The acceleration of the block relative to the incline is
A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly each after with a velocity of 12m/s, then the velocity of the third part which has 3 times mass of each part is
A cricket ball of mass 150 g has an initial velocity u = ( 3 i ^ + 4 j ^ ) ms – 1 and a final velocity v = – ( 3 i ^ + 4 j ^ ) ms – 1 , after being hit. The change in momentum (final momentum – initial momentum) is (in kg-ms -1 )
A space craft of mass ‘M’ and moving with velocity ‘v’ suddenly breaks in two pieces of same mass m. After the explosion one of the mass ‘m’ becomes stationary. What is the velocity of the other part of craft
A shell is fired from a cannon with velocity v m/sec at an angle θ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in m/sec of the other piece immediately after the explosion is
A batsman hits a sixer and the ball touches the ground outside the cricket ground. Which of the following graph describes the variation of the cricket ball’s vertical velocity v with time between the time t 1 as it leaves the bat and time t 2 when it touches the ground
A force-time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and 8 second is
A rope of length L and mass M is hanging from a rigid support. The tension in the rope at a distance x from the rigid support is
A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is
In the figure, pulleys are smooth and strings are massless, m 1 = 1 kg and m 2 = 1 3 kg To keep m3 at rest, mass m 3 should be
A body of mass M at rest explodes into three pieces, two of which of mass M /4 each are thrown off in perpendicular directions with velocities of 3 m s – 1 and 4 m s – 1 , respectively. The third piece will be thrown off with a velocity of
Two masses m and M are attached with strings as shown. For the system to be in equilibrium, we have
A man of mass m has fallen into a ditch of width d . Two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Both the friends exert force of equal magnitudes F . When the man is at a depth h , the value of F is
Two blocks of masses M and m are connected to each other by a massless string and spring of force constant k as shown in the figure. The spring passes over a frictionless pulley connected rigidly to the edge of a stationary block A . The coefficient of friction between block M and the plane horizontal surface of A is μ . The block M slides over the horizontal top surface of A and block m slides vertically downwards with the same speed. The mass M is equal to
A sphere of mass m is held between two smooth inclined walls. For sin37° = 3 5 , the normal reaction of the wall (2) is equal to
Two forces are acting on a rope lying on a smooth table as shown in figure. Which of the following statement (s) is/are correct? I. In moving from A to B, tension on string decreases from 2F to F. II. Situation will becomes indeterminant, if we take it a massless string.
In the diagram shown in figure, match the following columns. (Take, g = 10 ms -2 ) Column I (A) Acceleration of 2 kg block (B) Net force on 3 kg block (C) Normal reaction between 2kg and 1 kg (D) Normal reaction between 3 kg and 2 kg Column II (p) 8 SI unit (q) 25 SI unit (r) 2 SI unit (s) 45 N (t) None
A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck, suddenly moves to the right with an acceleration of a. The pendulum will tilt
A particle moving with velocity ν is acted by three forces shown by the vector triangle PQR. The velocity of the particle will [NEET 2019]
A gun applies a force F on a bullet which is given by F = 100 – 0 . 5 × 10 5 t N . The bullet emerges out with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero. [AIIMS 2019]
Assertion Even though net external force on a body is zero, momentum need not to conserved. Reason The internal interaction between particles of a body cancels out momentum of each other. [AIIMS 2019]
A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is
In the figure, mass of a ball is 9 5 times mass of the rod. Length of rod is 1 m. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod. [AIIMS 2018]
A force of 10 N acts on a body of mass 0.5 kg for 0.25s starting from rest. What is its impulse?
A mass M is hung with a light inextensible string as shown in the figure. Find the tension of the horizontal string.
Two masses 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown in figure, the 10 kg mass has acceleration of 12 m/s 2 . The value of acceleration of 20 kg mass is
Block B lying on a table weighs w. The coefficient of static friction between the block and the table is μ . Assume that the cord between B and the knot is horizontal. The maximum weight of the block A for which the system will be stationary is
A balloon with mass m is descending down with an acceleration a (where, a < g). How much mass should be removed from it, so that it starts moving up with an acceleration a ?
A bullet moving with a velocity of 30 2 ms -1 is fired into a fixed target. It penetrated into the target to the extent of s meter. If the same bullet is fired into a target of thickness s 2 metres and of the same material with the same velocity, then the bullet comes out of the target with velocity, is [EAMCET 2014]
Three identical blocks of masses m = 2 kg are drawn by a force 10.2 N on a frictionless surface. What is the tension (in newton) in the string between the blocks B and C ?
Three blocks with masses m , 2 m and 3 m are connected by strings as shown in the figure. After an upward force F is applied on block m , the masses move upward at constant speed v . What is the net force on the block of mass 2 m ? ( g is the acceleration due to gravity)
A 60 kg person is weighed by a balance as 54 kg in a lift which is accelerated downwards. The acceleration of the lift is
A lift starting from rest with a constant upward acceleration moves 1.5 m in 004 s. If a person standing in the lift holds a packet of 2 kg by a string, then the tension in the string due to motion is [UP CPMT 2013]
A body of mass 0.25 kg is projected with muzzle velocity 100 m s – 1 from a tank of mass 100 kg. What is the recoil velocity of the tank?
A machine gun fires a bullet of mass 40 g with a velocity 1200 m s – 1 .The man holding it can exert a maximum force of 144 N on the gun. How many bullets can be fired per second at the most?
Diwali rocket is ejecting 50 g of gases/s at a velocity of 400 ms -1 . The accelerating force on the rocket will be [RPMT 2011]
A rocket of mass 1000 kg is to be projected vertically upwards. The gases are exhausted vertically downwards with velocity 100 m s – 1 with respect to the rocket. What is the minimum rate of burning of fuel, so as to just lift the rocket upwards against the gravitational attraction? (Take, g = 10 m s – 2 ) [AMU 2011]
A plumb line is hanging from the ceiling of a train. If the train moving along a horizontal track with a uniform acceleration a, the plumb line gets inclined to the vertical at an angle θ is given by
A train rounds an unbanked circular bend of radius 50 m at a speed of 54 kmh -1 . If g = 10 ms -2 , the angle of banking required to prevent wearing out of rails is given by θ = tan − 1 ( p ) . The value of p is
An aeroplane of mass M requires a speed v for take off. The length of the runway is s and the coefficient of friction between the tyres and the ground is μ . Assuming that the plane accelerates uniformly during the take-off, the minimum force required by the engine of the plane for take-off is given by
A car moving at a speed v is stopped by a retarding force F in a distance s. If the speed of the car was 3v, the force needed to stop it within the same distance s will be
A car, moving at a speed of 54 kmh -1 , is to go round a curved road of radius 30 m. If the curved road is not banked, what must be the coefficient of friction between the tyres and the road for the car to negotiate the curve? Take g = 10 ms -2
In the arrangement shown in fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M rnoves upwards with a speed
The masses of 10 kg and 20 kg respectively are connected by a massless spring in fig. (4). A force of 200 newton acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration 12 m/sec 2 . What is the acceleration of 20 kg mass ?
A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be
Two blocks of masses 2 kg and 1 kg are placed on a smooth horizontal table in contact with each other as shown fig. A horizontal force of 3 newton is applied on the first so that the block moves with a constant acceleration. The force between the blocks would be
Two masses each equal to m are lying on X-axis at (- a,0) and (+ a, 0) respectively as shown in fig. They are connected by a light string. A force F is applied at the origin and along the Y-axis. As a result, the masses move towards each other What is the acceleration of each mass ? Assume the instantaneous position of the masses as (- x,0) and {x, 0) respectively
A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle θ without changing its speed. The impulse imparted to the ball is
The elevator shown in fig. is descending with an acceleration of 2 m/s 2 . The mass of the block A = 0.5 kg. The force exerted by the block A, on block B is
A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2 : 1 . What will be the ratio of their nuclear size (nuclear radius) ?
Consider the system shown in fig. The pulley and the string are light and all the surfaces are frictionless. The tension in the string is (take g = 10 m/s 2 )
A projectile is projected with a linear momentum p making an angle θ with the horizontal. The change in momentum of the projectile on return to the ground will be
In the following fig., pulley is massless and frictionless there is no friction between the body and the floor. The acceleration produced in the body when it is displaced through a certain distance will be
A satellite in force-free space sweeps stationary interplanetary dust at a rate of (dm / dt) = α v where m is mass and v is the speed of satellite and a is a constant. The deceleration of the satellite is
A machine gun is mounted on a 200 kg vehicle on a horizontal smooth road (friction negligible). The gun fires 10 bullets per second with a velocity of 500 m/s. If the mass of each bullet be 10 g, what is the acceleration produced in the vehicle ?
A balloon has 8 g of air. A small hole is pierced into it. The air escapes at a uniform rate of 7 cm/s. If the balloon shrinks in 5 .6 second, then the average force acting on the balloon is
A body of mass M at rest explodes into three pieces, two of which of mass M/4 each, are thrown off in perpendicular directions with velocities of 3 m,/s and 4 m/s respectively, The third piece will be thrown off with a velocity of
n balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will be
A player caught a cricket ball of mass l50 g moving at a rate of 20 m/s. If the catching process is completed in 0 . l second, the force of blow exerted by the ball on the hand of the player is equal to
A light spring balance hangs from the hook of the other light balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is
A 3000 kg space probe is moving in a grayity free space at a constant velocity of 300 m/s. To change the direction of space probe, rockets have been fired in a direction perpendicular to the direction of initial motion of the space probe, the rocket firing exerts a thrust of 4000 N for 225 s. The space probe will turn by an angle of (neglect the mass of the rockets fired)
A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20m / s 2 , the amount of gas ejected per second to supply the needed thrust will be (g = 10m/s 2 )
A smooth inclined plane of length l, having an inclination θ with horizontal is inside a lift which is moving down will retardation a. The time taken by a body to slide down the inclined plane from rest will be
A jet of water with a cross-sectional area a is striking against a wall at an angle θ to the horizontal and rebounds elastically. If the velocity of water jet is v and the density is ρ , the normal force acting on the wall is
Two masses of 10 kg and 5 kg are suspended from a fixed support as shown in fig. The system is pulled down with a force of 150 N attached to the lower mass. The string attached to the support breaks and the system accelerates downwards, If the downwards force continues to act, what is the acceleration of the system ?
Two weights W 1 and W 2 are attached to the ends of a string which passes over a frictionless pulley. If the pulley is placed in a rocket accelerating upwards at 9.8 m/s 2 , the tension in the string would be (take g = 9.8 m/s 2 )
A block is dragged on a smooth plane with the help of a rope which with a velocity v as shown in fig. The horizontal velocity of the block is
In fig., the blocks are of equal mass. The pulley is fixed. In the position shown, A moves with a speed u and the speed of B is v. Then
The surfaces are frictionless, the ratio of T 1 and T 2 is
With reference to fig. showing a light inextensible showing passing over a fixed frictionless pulley, the tension T 3 is
A mass M of 100 kg is suspended with the use of strings A, B and C as shown in fig. Here W is vertical wall and of is rigid horizontal rod. The tension in string B is
The pulleys and strings shown in fig. are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be
A 3 kg ball strikes a heavy rigid will with a speed of 10 m/s at an angle of 60″. It gets reflected with the same speed and angle as shown in fig. If the ball is in contact with the wall for0.20 s, what is the average force exerted on the ball by the wall ?
The linear mass density, i.e., mass per unit length of the rope shown in fig. varies 0 to λ from one end to another. The acceleration of the combined system of figure will be
Three masses of 16, 8, and 4 kg are placed in contact with each other as shown in fig. If a force of 140 N is applied on 4 kg mass, then force on 16 kg mass will be
A machine gun fires a bullet of mass 40 g with a velocity 1200 m/s. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
The aeroplane of mass M requires a speed v for take-off. The length of the run-way is s and the coefficient of friction between the tyres and ground is µ. Assuming that the plane accelerates
If P x =2 sin t and p y = 2cost, then the angle between linear momentum p and force F will be
A block A of mass M rests on a wedge B of mass 2 M and inclination θ . There is sufficient friction between A and B, so that A does not slip on B . If there is no friction between B and ground, the compression in spring is
In the figure, the coefficient of friction between the floor and the block B is 0.1. The coefficient of friction between the blocks B and A is 0.2. The mass of A is m/2 and of B is m. What is the maximum horizontal force F which can be applied to the block B so that two blocks move together?
Natural length of the spring is 40 cm and its spring constant is 4000 N m -1 . A mass of 20 kg is hung from it. The extension produced in the spring is (Given g = 9.8 m s -2 )
A car passes along a curved path of a road according to figure moving with speed of 72 km h -1 , radius of curve is 10 m. If mass of the car is 500 kg, reaction force (in kN) on car at lowest point of curved part will be .
Figure shows block A a motor C mounted on a with combined mass m and another block B of mass 2m. Block B is attached to shaft of motor with a light inextensible string. Motor is switched on at t =0 and string starts winding on its shaft and block B starts moving at acceleration a. If initial separation between blocks is l then find the time after which the two bodies will collide. The friction coefficient between blocks and ground is μ .
A hose directs a horizontal jet of water moving with a velocity of 20 m/sec on to a vertical wall. The cross sectional area of the jet is 5 x 10 –4 m 2 . If the density of water is 10 3 kg/m 3 , find the force on the wall assuming that the water is brought to rest there
A meal plate of mass 500 g is balanced in mid air by throwing 20 balls per sec, each of mass 5 g vertically up from below, which gets rebounced with the same speed. Find the velocity with which the balls strike the plate (g = 9.8 m/sec 2 )
A body of mass ‘m’ falls from a height h 1 and rises to a height ‘h 2 ’. The magnitude of the change in momentum during the impact with ground
Two masses A and B of 5 kg and 6 kg respectively are connected by a string passing over a frictionless pulley fixed at the corner of table as shown in the figure. The coefficient of friction between A and the table is 0.3. Find the minimum mass of C (in kg) that must be placed on A to prevent it from moving (Take g = 10 m/s 2 ).
Normal reaction on the block is ……… if the block is as shown in the figure.
A force F is applied on a rope of length L placed on ground as shown in the figure. Then tension in the rope at P………………
In a foot ball match a ball is kicked by a player with a force of 25 N for 0.2 s and then by another player with a force of 70 N for 0.1 s in the same direction. If the ball gains a velocity of 24 m/s after two kicks, the mass of ball is
Ten coins are arranged one above the other. The mass of each coin is 10 g. The reaction force on the sixth coin from the bottom of the seventh coin is (g = 9.8 m/sec 2 ) counting from the bottom
A body of mass ‘m’ falls from a height h 1 and rises to a height ‘h 2 ’.The magnitude of the change in momentum during the impact with ground
A meal plate of mass 500 g is balanced in mid air by throwing 20 balls per sec, each of mass 5 g vertically up from below, which gets rebounced with the same speed. Find the velocity with which the balls strike the plate (g = 9.8 m/sec 2 )
A body with mass 5kg is acted upon by a force f = ( − 3 i ^ + 4 j ^ ) N . If its initial velocity at t=0 v = ( 6 i ^ − 12 j ^ ) ms − 1 , the time at which it will just have a velocity along the y axis is
In figure, the acceleration of A is a A = 15 i ^ + 15 j ^ . Then the acceleration of B is (A remains in contact with B)
A machine gun fires a steady stream of bullets at the rate of n per minute into a stationary target in which the bullets get embedded. If each bullet has a mass m and arrives at the target with a velocity v, the average force on the target is
A machine gun fires a bullet of mass 40 g with a velocity 1200 ms – 1 . The man holding it, can exert a maximum force of 144 N on the gun. How many bullets can be fired per second at the most?
10000 small balls, each weighing 1 g, strikes 1 cm 2 of area per second with a velocity 100 ms – 1 in a normal direction and rebound with the same velocity. The value of pressure on the surface will be
A train of mass M is moving on a circular track of radius R with constant speed v. The length of the train is half of the perimeter of the track. The linear momentum of the train will be
An object of mass 5 kg is moving with a constant velocity of 10 m s -1 . A constant force acts on it opposite to its velocity 4 seconds and gives it a velocity of 2 m s -1 in the opposite direction. The acceleration produced by the force is
A body of mass 2 kg moving on a horizontal surface with an initial velocity of 4 m/sec comes to rest after 2 sec. If one wants to keep this body moving on the same surface with a velocity of 4 m/sec, the force required is
A bullet of mass 10 -3 kg strikes an obstacle and moves at 60° to its original direction. If its speed also changes from 20 m/s to 10 m/s , the magnitude of the impulse acting on the bullet is
A body of mass 1kg is moving with velocity 30 ms -1 due north. It is acted on by a force of 10N due east for 4 seconds. Find the velocity of the body after the force ceases to act
A ball of mass 0.1 kg strikes a wall normally with a speed of 30 ms -1 and rebounds with a speed of 20 ms -1 . The impulse of the force exerted by the wall on the ball is
A force produces an acceleration of 4 m s -2 in a body of mass m 1 kg and the same force produces an acceleration of 6 m s -2 in another body of mass m 2 . If the same force is applied to (m 1 + m 2 ), then the acceleration will be
If masses of blocks A and B are 3 kg and 8 kg respectively, then normal reaction between A and B
If the average velocity of a body moving with uniform acceleration under the action of a force is “v” and the impulse it receives during a displacement of “s” is “I”. The constant force acting on the body is given by
The linear momentum of a particle is given by p = a + bt 2 where t is time and a and b are constants. The force acting on the body varies directly as
A body of mass 1kg is moving with velocity 30 ms -1 due north. It is acted on by a force of 10N due east for 4 seconds. Find the velocity of the body after the force ceases to act
A cricket player catches a ball of mass 10 -1 kg, moving with a velocity of 25 ms -1 . If the ball is caught in 0.1 s, the force of the blow exerted on the hand of the player is
Starting from rest a 5 kg body gains a velocity of v ¯ = ( 3 i ^ + 4 j ^ ) m / s , in 2.5 S. Then average force acting on the body is
A force produces an acceleration of 4 m s -2 in a body of mass m 1 kg and the same force produces an acceleration of 6 m s -2 in another body of mass m 2 . If the same force is applied to (m 1 + m 2 ), then the acceleration will be
A ball of mass 500 gm is moving with velocity 2 m/s along a straight line. A constant force of 2 N acts on the ball for 2S in a direction opposite to the motion of the ball. Then final velocity of the ball is
A ball of mass 0.1 kg strikes a wall normally with a speed of 30 ms -1 and rebounds with a speed of 20 ms -1 . The impulse of the force exerted by the wall on the ball is
A 150 g cricket ball, moving horizontally at 20 m/s was hit straight back to the bowler at 12 m/s. If contact with the bat lasted for (1/25) sec, the average force exerted by the bat on the ball is
If the average velocity of a body moving with uniform acceleration under the action of a force is “v” and the impulse it receives during a displacement of “s” is “I”. The constant force acting on the body is given by
A dish of mass 10 g is kept floating horizontally in the air by firing bullets each of mass 5 g with the same velocity. If 10 bullets are fired per second and the bullets rebound with the same velocity, then the velocity of each bullet is
A ball of 0.5 kg collided with wall at 30° with the normal at the point of contact with the wall and bounced back elastically. The speed of ball was 12 ms – 1 . The contact remained for Is. What is the force applied by wall on ball? [JIPMER 2018]
A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below. If the mass of each marble is 5 g. What will be velocity with which the marbles are striking the disc? Assume that, the marble strikes the disc normally and rebound downwards with the same speed.
Starting from rest a 5 kg body gains a velocity of v ¯ = ( 3 i ^ + 4 j ^ ) m / s , in 2.5 S. Then average force acting on the body is
A ball of mass 500 gm is moving with velocity 2 m/s along a straight line. A constant force of 2 N acts on the ball for 2S in a direction opposite to the motion of the ball. Then final velocity of the ball is
The linear momentum of a particle is given by p = a + bt 2 where t is time and a and b are constants. The force acting on the body varies directly as
Three blocks with masses m , 2 m and 3 m are connected by strings as shown in the figure. After an upward force F is applied on block m , the masses move upward at constant speed v . What is the net force on the block of mass 2 m ? ( g is the acceleration due to gravity)
A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength is 75% of the weight of the monkey; the minimum acceleration with which the monkey can slide down without breaking the branch is:
Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be
A block of mass m is projected up an inclined plane of inclination θ with an initial velocity u. If the coefficient of kinetic friction between the block and the plane is μ = tan θ , the distance up to which the block will rise up the plane, before coming to rest, is given by
A body of mass 1 kg initially at rest, explodes and breaks into three fragments of masses in the ratio 1 : 1: 3. The two pieces of equal mass fly off perpendicular to each other with a speed of 15 ms -1 each. What is the velocity of the heavier fragment?
A body of mass 40 kg resting on a rough horizontal surface is subjected to a force P which is just enough to start the motion of the body. If μ s = 0 .5 , μ k = 0 .4 , g = 10 ms − 2 and the force P is continuously applied on the body, then the acceleration of the body is
A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is
When forces F 1 , F 2 , F 3 are acting on a particle of mass m such that F 2 and F 3 are mutually perpendicular, then the particle remains stationary. If the force F 1 is now removed then the acceleration of the particle is :
A mass M is hung with a light inextensible string as shown in the figure. Find the tension of the horizontal string.
A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s 2
A block of mass m = 2 kg is resting on a rough inclined plane of inclination 37 0 . The coefficient of friction between the block and the plane is μ = 0.5. What minimum force F (in newton) should be applied perpendicular to the plane on the block, so that the block does not slip on the plane?
As shown in figure, if acceleration of M with respect to ground is 2 ms -2 , then
Which of the following is correct, when a person walks on a rough surface
A rocket of mass 100 kg burns 0.1 kg of fuel per sec. If velocity of exhaust gas is 1 km/sec, then it lifts with an acceleration of
A block of metal weighing 2 kg is resting on a frictionless plane. It is struck by a jet releasing water at the rate of 1 kgs –1 and with a speed of 5 ms –1 . The initial acceleration of the block is
A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 ms – 1 . If the mass of the ball is 0.15 kg, the impulse imparted to the ball is
A rocket of mass 1000 kg is to be projected vertically upwards. The gases are exhausted vertically downwards with velocity 100 ms –1 with respect to the rocket. What is the minimum rate of burning of fuel, so as to just lift the rocket upwards against the gravitational attraction? (take g =10 ms –2 )
Gravels are dropped on a conveyor belt at the rate of 0.5 kg/sec. The extra force required in newtons to keep the belt moving at 2 m/sec is
A block of mass 3 kg rests on a horizontal frictionless xy-plane. What would be the acceleration of the block if it is subjected to two forces as shown in figure?
A rocket has total mass 1000 kg with fuel of 900 kg. It ejects fuel at the rate of 1 kg/s with an exhaust velocity of 2 km/s relative to rocket. The maximum velocity attained by rocket is
wo wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to block of mass M as shown in the figure. The magnitude of force P is
The principle of rocket motion is based on
A force of magnitude 10 N acts on a body at rest for 3 sec but the body is continued to move on horizontal floor. Velocity of the body at 6 sec is ms − 1 if mass of the body is 2 kg.
A block is dragged on a smooth plane with the help of a rope which moves with a velocity ν as shown in figure. The horizontal velocity of the block is
Two masses M and M/2 are joined together by means of light inextensible string passes over a frictionless pulley as shown in figure. When bigger mass is released, the small are will ascend with an acceleration of
