Important Work Power Energy Questions for CBSE Class 11th

A particle moves in the x-y plane under the action of a force F such that the value of its linear momentum P at any time t is P x = 2 cos t , P y = 2 sin t . The angle θ between F and P at a given time t will be

Two springs A and B with spring constant 2K and K are stretched separately by some force F. Then the ratio of work done in stretching A to that in stretching B is

Concrete blocks of masses m A and m B are balanced on two identical vertical springs. m A = 2 m B . The gravitational potential energy of each system is zero at the equilibrium position of the springs. Which statement is true for the total mechanical energy of the systems when the blocks are balanced on the springs?

A tank of size 10 m × 10 m × 10 m is full of water and built on the ground. If g = 10 m s – 2 , the potential energy of the water in the tank is

A juggler throws continuously balls at the rate of three in each second each with a velocity of 10 m s –1 . If the mass of each ball is 0.05 kg his power is

A body of mass 2 kg is being dragged with uniform velocity of 2 m/s on a rough horizontal plane. The coefficient of friction between the body and the surface is 0.20. The amount of heat generated in 5 sec is J = 4 .2 joule / cal and g = 9 .8 m / s 2

A particle can move along x-axis under the action of conservative force and its potential energy at any position is given by U = ( x 2 − 2 x + 16 ) J . Then the particle is in stable equilibrium at

A block of mass 4 kg rests on a horizontal surface. A vertically upward force of 52 N is applied on the block. If g = 10 m / s 2 , the work done by the applied force in 2 S is

A light and a heavy body have equal momenta. Which one has greater kinetic energy?

Two masses of 1 g and 4 g are moving with KE in the ratio of 4 : 1. What is the ratio of their linear momenta?

When the velocity of a body is doubled:

A force F =(2i+2k) dyne displaces a particle by an amount d = (2 i + 2j) cm in 16 sec. The power developed by the force F is

A force of F = 2 i ^ + 3 j ^ acting on a body mass 2kg which was initially at rest. If the displacement produced by the force is 12 i ^ +8 j ^ .Then the final velocity of the body is

A ball of mass m is thrown vertically up in air from the ground with initial speed u and is found to return to the starting point with a lesser speed of v. If g is the acceleration due to gravity, the maximum height reached by the ball is

A particle is at rest at the origin. Mass of the particle is 2 kg. It is displaced by 4m along the x-axis under the influence of a force F = ( 2 x ) i ^ N , then find velocity of the particle is

A block of mass 5 kg is moving in x-direction with a constant speed of 10 m/s. it is subjected to a retarding force F = − 0.2 x N during its travel from x=20 m to x=30 m. its final kinetic energy will be

A body projected obliquely with velocity 19.6 m/s has its kinetic energy at the maximum height equal to 3 times its potential energy there. Its position after 1second of projection from the ground is (h = maximum height)

A body is moving up an inclined plane of angle θ with an initial kinetic energy E. The coefficient of friction between the plane and body is µ . The work done against friction before the body comes to rest is

The total workdone on a particle is equal to change in its kinetic energy

The work done by the external forces on a system equals the change in

A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain onto the table ? (g = 10 m/ s – 2 )

Statement A : An engine A can perform a given work in 1 hr and engine B can perform the same work in ½ hr then B has greater power than A. Statement B : Power is the dot product of force and velocity

A running man has half the kinetic energy than a boy of half his mass has. The man speeds up by I m/sec and then has the same kinetic energy as the boy. What were the original speeds of man and boy respectively?

A block of mass 2 kg is dropped from a height of 40 cm on a spring whose force-constant is 1960 N m – 1 . The maximum distance through which the spring is compressed by

A particle moves 3m along the straight line x – y + 8 = 0 with constant speed under the influence of a constant force F = a i ^ − 3 j ^ N . Then the value of ‘a’ is

Mass of bob of a simple pendulum is 10 gm. It makes 10 oscillations in 15 seconds passes the mean position with a speed 4 cm/sec, work done by the tension in the suspension thread in oscillation is :

A block of mass 15 kg rests on a rough horizontal surface having coefficient of friction 0.6 between the block and the surface. A machine, delivering a constant power of 900 watt starts moving the block on the surface. Then maximum velocity of the block is

A box of mass 1 kg is pulled through 1 m along a level floor by a horizontal force of 8 N. The box is then raised vertically on to a bench 2 m high. If g = 10 ms -2 ,the total work done on the box is

A particle of mass 0.5 kg is moving along x-axis and at time t, its velocity is V = 5 t m/s where t is time in second. Then work done by the applied force in the time interval t = 1 sec to t = 2 sec is

A particle of mass 0.5 kg is at rest at the origin. If starts moving along x-axis under the influence of a force F = F i ^ where F varies with displacement x according to the graph shown in figure. Then kinetic energy of the particle at x = 3m is

A block B of mass 2 kg is placed on the rough inclined surface of a wedge W. The wedge is kept on a smooth horizontal floor and held in position by an external agent. The block is in equilibrium on the wedge. If the wedge slowly moves to the left by 5m,

A pendulum bob of mass 500 gm is suspended by a string of length 2 m. A horizontal force slowly displaces the bob from position A to position B as shown in the figure. Then work done by the applied force is …….if g=10 m s – 2

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? (g = 10 m/s 2 )

If a force F is applied on a body and it moves with a velocity v, the power will be

Two bodies of masses m and 4 m are moving with equal K.E. The ratio of their linear momenta is

The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of the kinetic energy obtained by measuring mass and speed

A position dependent force, F = 7 − 2 x + 3 x 2 newton acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m The work done in Joule is

, A uniform rod of mass m and length / is held inclined at an angle of 60 0 with the vertical. What will-be potential energy of the rod in this position ?

A long spring is stretched by 2 cm. Its potential energy is U. If the spring is stretched by 10 cm, the potential energy stored in it will be

A spring is held compressed. Its stored energy is 2. 4 joule. Its ends are in contact with masses of 1 gm and 48 gm placed on a smooth horizontal surface. When the spring is released, the mass will acquire a velocity of

A body of mass 3 kg is under a force which causes a displacement in it, given by s =t 2 / 3 (in m). Find the work done by the force in 2 second

A force F = 20 + 10 y acts on a particle in y -direction, where F is in newton and y is in metre. Work done by this force to move the particle from y = 0 to y = 1 m is [NEET 2019]

A body of mass 1 kg begins to move under the action of a time dependent force F = 2 t i ^ + 3 t 2 j ^ N , where i ⏜ and j ⏜ are unit vectors along X and Y -axis. What power will be developed by the force at the time (t)?

A body can have

When a wound spring is dissolved in an acid, the temperature of the acid

A chain of mass m and length ‘L’ is over hanging from the edge of a smooth horizontal table such that 3/4th of its length is lying on the table. The work done in pulling the chain completely on to the table is

The power of a crane is 6.25 kW. How much mass in kg of coal it can lift in 1 hour from a mine of 100 m depth? The efficiency of the crane is 80%

The motor connected to A (not shown) is pulling up the 200 kg block along the rough incline with constant speed of 5 m/s when power output of motor is 10 kW. If the power out put of motor is suddenly increased to 15 kW then the acceleration of block just after increasing the power is.

A force F ¯ = ( y 2 − x 2 + z 2 ) i ^ + ( 3 xy − 5 z ) j ^ + 4 z k ^ is applied on a particle from the point (0,0,0) to the point (2,4,0) in the path shown . If W A is the work done by the force in the paths A, then W A =?

Consider the system shown below, with two equal masses m and a spring with spring constant K. The coefficient of friction between the left mass and horizontal table is μ = 1 4 , and the pulley is frictionless. The string connecting both the blocks is massless and inelastic. The system is held with the spring at its unstretched length and then released. The extension in spring when the masses come to momentary rest for the first time is

The velocity time graph of a 2kg body is shown. Then the wrong statement is

A block of mass m is attached with a spring of force constant K. Now the other end of the spring is pulled with constant speed u. What is the maximum K.E of the block? ( μ = 0 )

In the graph shown the force F on a particle due to a conservative field is plotted against its position ‘x’ measured from origin. Which of the following statement is correct?

A particle can move along x-axis initially. The particle is at rest at the origin and force F = 2 t i ^ N is applied on it. If mass of the particle is 1 kg, the work done by the force in 2 second is

Two blocks of masses 2 kg an 4 kg are connected to the free ends of a spring of force constant 800N/m. The blocks are pulled apart so that the spring is stretched by a length ‘x’m. and are released simultaneously, When the spring acquires its natural length, velocity of 2 kg block is 4m/s. Then ϕ elastic potential energy stored in the spring just after the blocks are released is (the surface is smooth)

A body is moving on a frictionless horizontal surface under the influence of a constant force F = 3 i ^ + 4 j ^ m / sec 2 . When the velocity of the body is 2 i ^ − 3 j ^ m its kinetic energy.

In the arrangement shown, on external agent slowly pulls the block P from A to B along the rough inclined surface AB. The coefficient of friction between the block and the wedge is 0.75. Then the ratio of changes in potential energy of the block to the work done by the agent is

Work done by an external agent in stretching a spring by 1 cm is 9 J, work done in stretching the same spring by 2 cm is 16 J. Then the work done in stretching the same spring by 3 cm is

A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it in time t is proportional to

A body is initially at rest. It under goes one dimensional motion with constant acceleration. The power delivered to it at time t is proportional to

A block of mass 'M' is lowered with the help of a rope of negligible mass through a distance 'd' with an acceleration of g/3 . Work done by the rope on the block is

A ladder 'AB' of weight 300N and length 5m is lying on a horizontal surface. Its centre of gravity is at a distance of '2m' from end A. A weight of 80N is attached at end B. The work done in raising the ladder to the vertical position with end 'A' in contact with the ground is,

A uniform rod of length 2m and mass 5kg is lying on a horizontal surface. The work done in raising one end of the rod with the other end in contact with the surface until the rod makes an angle 30 0 with the horizontal is, (g = 10 m s – 2 ) .

The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle, then power developed by air is

One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is . The possible cases are a) the spring was initially compressed by a distance x and was finally in its natural length b) it was initially streched by a distance x and finally was in its natural length c) it was initially in its natural length and finally in a compressed position d) it was initially in its natural length and finally in a stretched position.

A body is moving under the expense of a constant power. If 'X' is the displacement in time 't', then 'x' is proportional to

The potential energy function for a particle executing linear SHM is given by where ‘k’ is the force constant of the oscillator. For k = 0.5Nm –1 , the graph of v(x) versus ‘x’ is shownn in figure. A particel of total energy ‘E’ turns back when it reaches x = ± x m . If V and k indicate the potential energy and kinetic energy, respectively of the particle at x = + x m , then which of the following is correct?

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, the average resistance offered by the wood to the blade is :

A particle is displaced along x-axis from x = 0 to x = 2 m under the influence of a force F = ( 2 x i ^ + 5 j ^ ) N . Then work done by the force is

An engine accelerates a car of mass 800 kg to a speed of 72 km/h. If the frictional force is 10 N per ton, the power developed by the engine is:

The power of a heart which pumps 5 × 10 3 cc of blood per minute at a pressure of 120 mm of mercury ( g = 10 ms – 2 ) and density of Hg = 13 . 6 × 10 3 kg / m 3 ) is

A pump motor is used to deliver water at a certain rate from a given pipe. To obtain, twice as much water from the same pipe, in the same time, the power of motor has to be increased to:

A 800 kg car moving with a velocity of 10 m/s along a straight road, doubles its velocity in 2 minutes. Then average power delivered by the engine in this interval is

A uniform chain of length 4m and mass 4 kg is placed on a smooth table with one-fourth of its length hanging over the edge. The work that has to be done to pull the whole chain back onto the table is

The potential energy of a particle varies with distance x as shown in the graph. The force acting on the particle is zero at

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. It losses 10% of energy due to frictional forces . How much power is generated by the turbine? (g = 10 m / s 2 )

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? (g = 10 m / s 2 )

Two similar springs P and Q have spring constants K p and K Q such that Kp > K Q . They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs W P and W Q are related as, in case (a) and case (b), respectively.

A block of mass l0 kg moving in x direction with a constant speed of l0 ms – 1 is subjected to a retarding force F = 0 . 1 x J / m during its travel from x = 20 m to 30 m. Its final KE will be

The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from

A system comprises of two small spheres with same masses ‘m’. Initially the spring is undeformed. The spheres are set in motion in gravity free space at the velocities as shown in the diagram. The maximum elastic potential Energy stored in the system is.

When a force is applied to a spring of force constant K, elongation produced in the spring is x. When the force is slowly increased to twice is present value, work done on the spring will be

A 4 kg block is projected with velocity 7 m/s up a rough inclined surface having inclination 45 o with horizontal. The block stops after travelling a distance of 2 2 m along the plane. Then coefficient of kinetic friction between the block and the plane is

A particle of mass 2 kg is at rest at point A (2m, 1m). It is displaced to point B (3m, 5m) under the action of a constant force F = 8 i ^ + 2 j ^ N . Then the rate at which the kinetic energy of the particle is increasing at point B is

Select the correct statement. In a conservative force field

A cork ball is tied to one end of a string and the other end of the string is tied to the bottom of a container filled with water as shown in figure. When the string is gently cut. The ball rises to position B where its velocity is V. Then

A block B of mass m is kept on the rough surface of a plank p, also of mass m. The plank is placed on a smooth horizontal floor. The block B is projected to the right with velocity V 0 on the plank. Work done by force of friction on B is W B and that on P is W P . Then

work done when a force F = ( i ^ + 2 j ^ + 3 k ^ ) N acting on a particle takes it from the point r 1 = ( i ^ + j ^ + k ^ ) to the point r 2 = ( i ^ – j ^ + 2 k ^ ) is:

A force F acting on an object varies with distance x as shown here. The force is in N and x is in m. The work done by the force in moving the object from x = 0 to x = 6m is :

A uniform force of ( 3 i ^ + j ^ ) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position ( 2 i ^ + k ^ ) meter to position ( 4 i ^ + 3 j ^ – k ^ ) meter. The work done by the force on the particle is

In the diagram shown, the pulley is very light. The particles are released from rest. When the heavier particle falls through a distance of 0.6 m, speed of the particles is

A block of mass 2 kg rests on ground. An external agent raises the block to a height of 5m above ground where its speed is V. It work done by the external agent is 200 J, value of V is

If F = ( 60 i ^ + 15 j ^ − 3 k ^ ) N and v = ( 2 i ^ − 4 j ^ + 5 k ^ ) m / s , then instantaneous power is :

A car of mass 800 kg is being driven with a constant acceleration 1.5 m/s2 on a straight road against a constant resistive force 72 N. When the speed of the car is 72 km/hr, the rate at which engine is doing work will be :

A body of mass 2 kg is projected at 20 m/s at an angle 60° above the horizontal Power due to the gravitational force on the block at its highest point is : (take g = l0 m/s 2 )

Velocity of a particle of mass I kg moving rectilinearly is given by , v = 25- 2t + t 2 . Find the average power of the force acting on the particle between time interval t = 0 to t = 1 sec.

The PE stored in a long spring stretched by 1 cm is U. If the spring is stretched by 3 cm instead, its PE will be :

The KE of a body moving with a speed of 10 m/s is 30 J. If its speed becomes 30 m/s, its KE will be :

A spring of spring constant 5 x 10 3 N/m is stretched initially by 5 cm from the upstretched position. Then work required to stretch it further by another 5 cm is :

Two springs A and B having spring constant K A and K B where K A = 2K B . These are stretched by applying force of equal magnitude. If energy stored in spring A is E then energy stored in B will be :

A particle of mass m 1 is moving with a velocity v 1 and another particle of mass m 2 is moving with a velocity v 2 . Both of them have the same momentum but their different kinetic energies are E 1 and E 2 respectively. If m 1 > m 2 then :

A ball of mass m is attached to a string whose other end is fixed. The system is free to rotate in vertical plane. When the ball swings, no work is done on the ball by the tension in the string. Which of the following statements is the correct explanation ?

Two bodies of masses m A and m B have equal KE. The ratio of their momenta is:

If the linear momentum of a body is increased by 50%, its KE will increase by:

If momentum of a certain body is increased by 50%then increase in the K.E. of the body will be

An open knife edge of mass M is dropped from a height I on a wooden floor. If the blade penetrates S into the wood, the average resistance offered by the wood to the blade is

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

A bullet of mas m moving horizontally with velocity v hits a block of wood of mass M, resting on a smooth horizontal plane. The fraction of energy of the bullet dissipated in the collision it self is (assume collision to be inelastic)

A crane is used to lift 10,000 kg of coal from a mine 100 meter deep. Time taken by the crane is one hour. Assuming the efficiency of the crane to be 80%, the power of the crane in kW is

The force constant of a weightless spring is 16 N/m. A body of mass 2.0 kg suspended from it is pulled down through 5 cm and then released. The maximum kinetic energy of the system (spring + body) will be

Consider the following two statements (A) Linear momentum of a system of particles is zero (b) Kinetic energy of a system of particles is zero’ Then

A body of mass m has a kinetic energy equal to one-fourth kinetic energy of another body of mass m/4′ If the speed of the heavier body is increased by 4 m/s, its new kinetic energy equals the original kinetic energy of the lighter body. The original speed of the heavier body in m/s is

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy K with the distance travelled x ?

A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments: one in which the charged particle is abo a proton and in another a positron. In the same time t , the work done on the two moving charged particles is [NCERT Exemplar]

A spring of spring constant 5×10 3 N/m is stretched initially by 5 cm from the unscratched position. Then the work required to stretch it further by another 5 cm is

A mass-spring system oscillates such that the mass moves on a rough surface having coefficient of friction μ . It is compressed by a distance a from its normal length and on being released, it moves to a distance b from its equilibrium position. The decrease in amplitude for one half-cycle (- a to b ) is

A force of 10i – 3j + 6 k newton acts on a body of 5kg and it displaces from 6i+5j-3k metre to 10 i -2j+7k metre. The work done is

Which of the following statement(s) is/are correct? I. If momentum of a body increases by 50%, its kinetic energy will increase by 125%. II. Kinetic energy is proportional to square of velocity.

A block of mass m is stationary with respect to a rough wedge is shown in figure. Starting from rest in time t m = 1 kg , θ = 30 ° , a = 2 ms – 2 , t = 4 s Match the following columns for work done on the block and mark the correct option from the codes given below. Column I (A) By gravity (B) By normal reaction (C) By friction (D) By all the forces Column II (p) 144 J (q) 32 J (r ) – 160J (s) 48 J

Two bodies of different masses are moving with same kinetic energy. Then, the ratio of their momenta is equal to the ratio of their [Kerala CEE 2015)

Kinetic energy of a particle is increased by 4 times. What will be the relation between initial and final momentum? [JIPMER 2018]

‘n’ identical cubes each of mass ‘m’ and side ‘l’ are on the horizontal surface. Then the minimum amount of work done to arrange one on the other is

A force F is acting at a on a body distance d from an axis as shown. The torque of this force about the given axis is

A metallic rod is rotating on a frictionless horizontal plane about an axis passing through one of its end, If the angular velocity is doubled

What is the radius of the circular orbit of a stationary satellite which remains motionless with respect to earth’s surface ?

A sphere of mass m, attached at its center to a spring on incline as shown in figure, is held in unstretched position of spring. Suddenly the sphere is set free, the maximum extension of spring is (friction is enough to prevent slipping)

A particle A of mass 10 7 kg is moving in the positive direction of X. Its initial position is x=0 and initial velocity is 1m/sec. The velocity at x = 10m is …..

A sphere of mass 2 kg is moving on a frictionless horizontal table with velocity v. It strike with a spring of constant 1 N/m and compresses it by 4 m. The velocity (v) of the sphere is :

A particle of mass 2 kg is moved along a line 3 y = 4 x + 10 under the influence of a force F = ( 4 i ^ − 3 j ^ ) N . Find the work done by the force between the points − 10 4 , 0 and 0 , 10 3

A particle of mass m is moving in a field. The potential energy vs position (x ) graph is given as shown in the diagram. The dotted horizontal line represents the total mechanical energy of the particle. Find in which region the particle will not exist?

A ring of linear mass density 2 λ and radius R is rotated about its axis passing through its centre and perpendicular to plane of ring with constant angular speed ‘ ω ’. The tension in the ring is

Power versus time graph for a given force is given below. Work done by the force upto time t ≤ t 0 .

A trolley of mass m is connected to two identical springs, each of force constant k, as shown in fig. The trolly is displaced from its equilibrium position by a distance x and released. The trolly executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)

Two cylindrical vessels of equal cross sectional area contain water up to heights h 1 > h 2 and h 2 . The vessels are inter connected so that the levels in them become equal. Calculate the work done by the force of gravity during this process if ρ is the density of water.

A body of mass 1 k g begins to move under the action of a time dependent force F = ( 2 t i ^ + 3 t 2 j ^ ) N , where i ^ a n d j ^ are unit vectors along x and y axis. What power will be developed by the force at the time t ?

A force F=20+10 y acts on a particle in y -direction where F is in newton and y in meter. Work done by this force to move the particle from y =0 to y =1 m is

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 × 10 – 3 kg/ m 3 and g = 10 m / s 2 then the power of heart in watt is

A ball is thrown vertically downwards from a height of 20 m with an initial velocity ν 0 . It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity ν 0 is (Take g = 10 ms – 2 )

Two springs of force constant 100 N/m and 150 N/m are in series as shown. The block is pulled by a distance of 2.5 cm to the right from equilibrium position. What is the ratio of work done on the spring at left to the work done on the spring at right?

The potential energy of a particle of mass 5 kg moving in the x-y plane is given by U = − 7 x + 24 y J , x and y being measured in metre. If the particle starts from origin from rest, then the magnitude of the conservative force acting on the particle is:

A uniform force of 3 i ^ + j ^ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position 2 i ^ + k ^ meter to position 4 i ^ + 3 j ^ − k ^ meter. The work done by the force on the particle is

A particle moves from a point ( – 2 i ^ + 5 j ^ ) to ( 4 j ^ + 3 k ^ ) when a force of ( 4 i ^ + 3 j ^ ) N is applied. How much work has been done by the force?

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is

A block of mass 10 kg , moving in x direction with a constant speed of 10 m s – 1 , is subjected to a retarding force F = 0.1 x J/m during its travel from x = 20 m to 30 m. Its final KE will be

Two similar springs P and Q have spring constants K p and K Q , such that K P > K Q . They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs W P and W Q are related as, in case (a) and case (b) respectively

What is the change in potential energy ( in calories) of a 10 kg mass after 41.8m of fall?

A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio

A body of mass m slides downward along a plane inclined at an angle α . The coefficient of friction is μ . The rate at which kinetic energy plus gravitational potential energy dissipates expressed as a function of time is

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m s – 1 . Take ‘g’ constant with a value 10 m s – 2 . The work done by the (i) gravitational force and the (ii) resistive force of air is

A bullet of mass ‘m’ is fired with a velocity ‘v’ into a block of wood of mass ‘M’ suspended by a thread. If the bullet gets embedded in the block it rises to a height of

A uniform chain of mass ‘m’ and length l is on a table with 1 4 of its length hanging freely from the edge of the table. The amount of work done is dragging the chain on to the table completely is

A force of F = 10 t + 3 t 2 is acting on a particle on a particle of mass 1Kg at rest, where F is in newton and t is in seconds. Work done by this force in first 1 second is

A car and a truck are moving with same kinetic energy. To stop them brakes exerting equal forces are applied simultaneously. Then, which of the following statements is correct?

A body of mass 2 kg moves down the quadrant of a circle of radius 4 m. The velocity on reaching the lowest point is 8 m s – 1 . Work done against friction is (take g = 10 m / s 2 )

A block of mass 2 kg is placed on a rough horizontal surface, coefficient of friction between the block and the surface is 0.4. A horizontal force of 10N is applied on the block. Then rate of work done by the force at t = 1 sec is (The 10 N force is applied at t = 0).

A body of mass 5 Kg is raised vertically to a height of 10m by a force 170N. The velocity of the body at this height will be

The force F acting on a body moving along x-axis varies with the position x of the particle as shown in the graph. The body is in stable equilibrium at

In figure shown, a carriage P of mass 50 kg is slowly pulled up from A to B. The relevant coefficient of friction is 0.40. Then the work done is

The system shown in Fig. is released from rest with mass 2 kg in contact with the ground. Pulley and spring are massless, and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with the ground is (force constant of the spring k = 40 N m – 1 and g = 10 m s – 2 )

Two balls of masses m 1 and m 2 are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass m 1 travels a distance s 1 and stops. If the coefficients of friction between the balls and ground are same, the mass m 2 stops after travelling the distance

System shown in figure is released from rest. Pulley and spring are mass less and the friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (take force constant of the spring K = 40 N/m and g = 10 m / s 2 )

Force acting on a particle moving in a straight line varies with the velocity of the particle as F = K/v, where K is a constant. The work done by this force in time t is

In position A kinetic energy of a particle is 60 J and potential energy is -20 J. In position B, kinetic energy is 100 J and potential energy is 40 J. Then, in moving the particle from A to B

If v, p and E denote velocity, linear momentum and KE of the particle then

A car of mass 1250 kg is moving at a speed of 30m/s. Its engine delivers power of 30kW while resistive force due to surface is 750 N.The maximum acceleration can be given to the car in m s – 2 is

A particle is projected with a velocity u making an angle θ with the horizontal. The instantaneous power of the gravitational force

Figure shows the vertical section of a frictionless surface. A block of mass 2 kg is released from rest from position A; its KE as it reaches position C is (g = 10 m s – 2 )

A 1-kg stone at the end of 1 m long string is whirled in a vertical circle at a constant speed of 4 m s – 1 . The tension in the string is 6 N when the stone is

The potential energy for a body of mass m that is acted on by a very massive body is given by U = – m g x + k x 3 3 . The corresponding force is

In the arrangement shown, There is no friction between the 4 kg block and the floor and friction exists at the interface of 2kg and 4kg blocks. If the blocks A and B move together without any relative motion between them, find the work done by the force of friction on block A in 2 second

A body of mass 1 kg is moving along positive x-axis with velocity 2 m/s. At t = 0, a constant force, parallel to positive y-axis, starts acting on the body and after 5 sec, speed of the body is found to be 4 m/s. Then work done by the force in 5 sec is

A particle of mass 0.2 kg is moving along x-axis and its displacement is given by x = 2 t 2 m , where t is time in second. Work done on the particle in 4 sec is

A particle of mass 2 kg starts moving from the origin along x-axis under the action of a force which is varying according to the graph shown in figure. Initial velocity of the particle is 2 m/s. Then work done by the force on the particle at t = 6 s is

A particle of mass 0.5 kg is moving in xy plane with acceleration a = 3 i ^ + 2 t j ^ m / s 2 . At time t, its velocity is given by V = 2 t i ^ + 3 t 2 j ^ m / s . Then rate of work done on the particle at t = 1 sec is

You crouch from standing position, lower your centre of mass by 20 cm and then jump vertically upward into the air. The average force that the ground exerts on you while you are jumping is three times your weight. Then the speed with which you leave the ground in standing position is

A particle moves with a velocity 6 i ^ − 4 j ^ + 3 k ^ m / s under the influence of a constant force F = 20 i ^ + 15 j ^ − 5 k ^ N . The instantaneous power applied to the particle is

Potential energy of a particle along x-axis varies as shown in the figure. If the particle is released from rest at a point on x-axis.

A gun of mass M fires a bullet of mass m horizontally with a Kinetic energy E. The velocity of recoil of the gun is

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown below correctly shows the displacement time curve for its motion ?

The given graph shows variation of potential energy with respect to position of the particle. The total mechanical energy of particle is also represented in the graph, region in which existence of particle is not possible

A bucket filled with water weighing 20 kg is slowly raised from a well of depth 20m. If the linear density of the rope is 0.2kg per meter, the amount of work done is, (g = 10m/ s 2 )

A vertical spring with force constant 'k' is fixed on a table. A ball of mass 'm' at a height 'h' above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance 'd'. The net work done in the process is

An engine pumps water continuously through a hose Water leaves the hose with a velocity 'v' and 'm' mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water

A rectangular block of dimensions 6m × 4m × 2m and of density 1.5 gm/c.c is lying on horizontal ground with the face of largest area in contact with the ground. The work done in arranging it with its smallest area in contact with the ground is, (g=10m s – 2 ) .

A force of (4x 2 + 3x) N acts on a particle which displaces it from x = 2m to x = 3m. The work done by the force is

The work done in lifting a body of mass 20kg and specific gravity 3.2 to a height of 8m in water is, (g = 10 m/ s 2 )

When a spring is compressed by 3cm, the potential energy stored in it is U. When it is compressed further by 3cm, the increase in potential energy is,

A simple pendulum is swinging in a vertical plane. The ratio of its potential energies when it is making angles 30 0 and 60 0 with the vertical is,

A 1.0 HP motor pumps out water from a well of depth 20m and fills a water tank of volume 2238 litres at a height of 10m from the ground. The running time of the motor to fill the emptytank is (g = 10 ms -2 )

A force applied by the engine of a train of mass 2.05 × 10 6 kg changes its velocity from 5ms –1 to 25ms –1 in 5 minutes. The power of the engine

A motor of power P 0 is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe n times, the power of the motor is increased to P 1 . The ratio of P 1 to P 0 is :

A man of mass 60kg lifts a 15kg mass to the top of a building of height 10m in 5 minutes. His efficiency is

A motor is used to lift water from a well of depth 10m and to fill a water tank of volume 30m 3 in 10 minutes. The tank is at a height of 20m above ground. If 20% of energy is wasted, the power of the motor is (in kW)

A bullet is fired from a rifle and the rifle recoils. Kinetic energy of rifle is

You lift a suitcase from the floor and keep it on a table. The work done by you on the suitcase does not depend on a) the path taken by the suitcase b) the time taken by you in doing so c) the weight of the suitcase d) your weight

Sand is falling on a conveyor belt at the rate of 5k g s – 1 . The extra power required to move the belt with a veloctiy of 6 m s – 1 is,

A man carries a load of 50 kg to a height of 40 m in 25s. If the power of the man is 1568W, the mass of the man is,

The radius of a well is 7m. Water in it is at a depth of 20m and depth of water column is 10m. Work done in pumping out water completely from the well is, (g = 10ms –2 )

Twenty identical cubical blocks each of mass 100gm and of side 10cm are lying on a horizontal surface. Work done in piling them one above the other is, (g = 10ms –2 )

A long rod ABC of mass “m” and length “L” has two particles of masses “m” and “2m” attached to it as shown in the figure. The system is initially in the horizontal position. The work to be done to keep it vertical with A at the bottom is (g = acceleration due to gravity)

A rectangular plank of mass 'm 1 ' and height 'a' is on a horizontal surface. On the top of it another rectangular plank of mass 'm 2 ' and height 'b' is placed. The potential energy of the system is,

A box of mass 50kg at rest is pulled up on an inclined plane 12m long and 2m high by a constant force of 100N applied parallel to the inclined plane. When it reaches the top of the inclined plane if its velocity is 2ms –1 , the work done against friction in Joules is (g = 10ms –2 )

A body of mass 1 kg begins to move under the action of a dependent force N are unit vectors along x and y axis. What power will be developed by the force in the time t?

A force F = 20 + 10y acts on a particle in y direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to y =1 m is

A spring of force constant 'k' is stretched by a small length 'x'. The work done in stretching it further by a small length 'y' is,

A body of mass 1kg is dropped from a height of 5m on to the ground.If the body penetrates 2cm in to the ground, the average resistance offered by the ground on to the body is (g = 10ms –2 )

A block of mass 'm' moving with a speed ' ' compresses a spring through a distance 'x' before its speed reduces by 25%. The spring constant of the spring is

In a hydel power project, 2000kg of water passes through the turbine every second. Water is falling from a height of 240m above ground. If the power output is 3.6 MW, the efficiency of the power house is (g= 10ms -2 )

A machine rated as 150W, changes the velocity of a 10kg mass from 4ms –1 to 10ms –1 in 4s. The efficiency of the machine nearly is

A rain drop of radius 2 mm falls from a height of 500m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains the maximum (terminal) speed and moves with uniform speed there after .What is the work done by the resistance force in the entire journey if its speed on reaching the ground is 10ms -1

Two bodies m 1 and m 2 are kept on a table with coefficient of friction ‘μ’ and are joined by a spring. Initially, the spring is in its relaxed state. The minimum constant force F which will make the other block m 2 move is ( k is the spring constant).

In the figure, the ball A is released from rest when the spring is unstretched. For the block of mass M to leave contact with ground at some stage, the minimum mass of A must be

A particle is at rest at the origin. A force A = ( a i ^ + b j ^ + 6 k ^ ) N is applied on the particle and it is displaced from the origin to the point (1, 2, 3) metre. For what values of ‘a’ and ‘b’, the particle will gain maximum kinetic energy?

Water is flowing in a river at 2 m s – 1 . The river is50 m wide and has an average depth of 5 m. The power available from the current in the river is (Density of water = 1000 kg m – 3 )

A car of mass 1000 kg accelerates uniformly from rest to a velocity of 54 km/h in 5 s. The average power of the engine during this speed is(neglect friction):

A light body A and a heavy body B have equal linear momentum. Then the KE of the body A is

A man M 1 of mass 80 kg runs up a staricase in 15 s . Another man M 2 also of mass 80 kg runs up the same staircase in 20 s. The ratio of the power developed by them will be:

Water is falling on the blades of a turbine from a height of 25 m. 3 × 10 3 kg of water pours on the blade per minute. If the whole of energy is transferred to the turbine, power delivered is: g = 9.8 m / s 2

An elastic spring of unstretched length L and force constant K is stretched by amount x. It is further stretched by another length y. The work done in the second stretching is

The work done by external agent in stretching a spring of force constant k from length l 1 to l 2 is

The work done by external agent in stretching a spring of force constant k = 100 N/m from deformation x 1 = 10 to deformation x 2 = 20 cm .

The potential energy of a spring when stretched through a distance x is 10 J. What is the amount of work done on the same spring to stretch it through an additional distance x?

A body starts from rest and acquires a velocity V in time T. The work done on the body in time t will be proportional to:

The displacement x in metres of a particle of mass m kg moving in one dimension under the action of a force is related to the time t in seconds by the equation t = x + 3 , the work done by the force (in J) in first six seconds is:

Under the action of a force, a 2 kg body moves such that its position x as a function of time t is given by x = t 3 3 , where x is in meter and t in seconds. The work done by the force in the first two seconds is:

Two identical 5 kg blocks are moving with same speed of 2 m/s towards each other along a frictionless horizontal surface. The two blocks collide, stick together and come to rest. Consider the two blocks as a system. The work done by external and internal forces are respectively:

A uniform chain of length 2m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. The work done in pulling the entire chain on the table is (Take g = ms – 2 )

Two springs have their force constant as k 1 and k 2 ( k 1 > k 2 ) . When they are stretched by the same force

The work done in dragging a stone of mass 100 kg up an inclined plane 1 in 100 through a distance of 10 m is (take g = 9.8 m / s 2 )

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where E is the total energy)

A 3 kg block is projected with a velocity of 4 m/s along a horizontal rough surface. The block stops after travelling some distance. The work done by frictional force is

The driver of a 1200 kg car notices that the car slows from 20 m/s to 15 m/s as it covers a distance of 125 m along level ground. How large a force opposes the motion?

When an automobile moves with constant speed down a highway, most of the power developed by the engine is used to compensate for the energy transformations due to friction forces exerted on the car by the air and the road. If the power developed by an engine is 175 hp, estimate the total friction force (approx.) acting on the car when it is moving at a speed of 25 m/s. One horsepower equals 746 W.

A pump motor is used to deliver water at a certain rate from a given pipe. To obtain ‘n’ times water from the same pipe in the same time, by what amount the power of the motor should be increased?

An electric pump on the ground floor of a building takes 10 minutes to fill a tank of volume 30 m 3 with water. If the tank is 60 m above the ground and the efficiency of the pump is 60%, how much electric power is consumed by the pump in filling the tank?

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13 . 6 × 10 3 kg / m 3 and g = 10 m / s 2 then the power of heart in watt is:

If force F is applied on a body and it moves with the velocity V, the power will be :

A projectile is launched at angle θ to the horizontal from point L and it hits the target on level ground. During the entire motion: Column-I Column-II i. Magnitude of radial acceleration p. remains constant ii. Magnitude of tangential acceleration q. always increases iii. Power delivered by gravity r. First increases, then decreases iv. Total acceleration s. First decreases, then increases Now match the given columns and select the correct option from the codes given below.

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is

A uniform force of ( 3 i ^ + j ^ ) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position ( 2 i ^ + k ^ ) metre to position ( 4 i ^ + 3 j ^ – k ^ ) metre. The work done by the force on the particle is

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is

A force F acting on an object varies with distance r as shown here. The force is in newton and x in metre. The work done by the force in moving the object from x = 0 to x = 6 m is

A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be:

In the figure shown initially spring is in unstretched state and blocks are at rest. Now 100 N force is applied on block A arrd B as shown in figure. After some time velocity of ‘A’ becomes 2 m/s and that of ‘ B’ 4 m/s and block A displaced by amount 10 cm and spring is stretched by amount 30 crn. Then work done by spring force on A will be:

A body of mass 5 kg is moving with a momentum of 10 kg-m/s. A force of 0.2 N acts on it in the direction of motion of the body for l0 seconds. The increase in its kinetic energy is

A body with mass 2 kg moves in one direction in the presence of a force which is described by the potential energy graph. If the body is released from rest at x = 2 m, then its speed when it crosses x = 5 m is

Block A of mass M in the figure is released from rest when the extension in the spring is x 0 . The maximum downward displacement of the block is (assume x 0 < Mg k )

A particle is acted upon by a force F which varies with position x as shown in figure. If the particle at x = 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x = 16 m is

The work done by the force = F = A ( y 2 i ^ + 2 x 2 j ^ ) , where A is a constant and x and y are in meters around the path shown is:

A force of F = 2 x i ^ + 2 j ^ + 3 z 2 k ^ N is acting on a particle. Find the work done by this force in displacing the body from (1, 2,3) m to (3, 6, 1) m.

An elevator can carry a maximum load of 1800 kg (elevator + passengers) is moving up with a constant speed of 2 ms – 1 . The frictional force opposing the motion is 4000 N. What is minimum power delivered by the motor to the elevator?

A force of F = 2 x i ^ + 2 j ^ + 3 z 2 k ^ N is acting on a particle. Find the work done by this force in displacing the body from (1, 2,3) m to (3, 6, 1) m.

A 1 kg mass is projected down a rough circular track (radius = 2.0 m) placed in vertical plane as shown. The speed of the mass at point A is 3 m/s and at point B, it is 6.0 m/s. How much work is done on the mass between A and B by the force of friction?

A bead X resting on a smooth horizontal surface, is connected to two identical springs and is made to oscillate to and fro along the line of the springs. When the bead passes through the central position. its energy is

A particle of mass 0. 1 kg is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at x = 0, its velocity at x = 12 m is

What is the average power output of an electric motor driving a pump for lifting 200 kg of water at a height of 100 m in 1 minute? Efficiency of pump is 75%

A particle is displaced from point A (2, 3) to point B (3, 2) under the influence of a constant force F = 3 i ^ + a j ^ N . If the speed of the particle remains unchanged, then value of ‘a’ is

A particle of mass m is attached to two vertical springs as shown in figure. Initially the particle is held in position by an external agent such that the springs are in their natural lengths. Now the particle is released. Then maximum elongation and compression produced in the upper and the lower springs respectively are

A particle can move along x-axis under the influence of a conservative force and variation of its potential energy is as shown in the figure. Then

An object is moving in a circle with constant speed. If F be the resultant force acting on the object, then the amount of work done on the object by this force is zero :

A chain is held on a frictionless table with one-third of its length hanging over the edge. If the chain has a length L and mass M, how much work is required to pull the hanging part back on the table?

A body is released from a height H. At some position during its free fall, its kinetic energy is two times its potential energy. Then height of the body at that instant is

A particle of mass ‘m’ is moving along X-axis under a force F = k x work done for the motion of particle from x = 4 m to x = 9 m is nearly:

Principle of conservation of energy

An object of mass 4 kg is moving along X-axis such that its position x varies with time t as x 2 = 16t 3 , with t in meter and r in sec. Work done as a function of time can be shown as :

In Figure, a block is pulled by a constant horizontal force on a smooth surface. Work done on the block as a function of speed acquired by the block can be described by :

An object of mass 6 kg is moved with uniform speed of 8 m/s for 8 sec on a surface. Coefficient of friction between the body and the surface is 0.6, work done for the given motion of the body is : (take g = 10 m/s 2 )

Two springs A and B have force constants k A and K B , respectively, with k A > K B . Both springs are stretched by the same force, then the work done is :

The force acting on an object varies with the distance travelled by the object as shown in Figure . Work done by the force in moving the object from x = 2 m to x=4 m is:

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is :

A particle of mass 100 g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time the particle goes up is :

A block rests on a rough horizontal surface. It is projected along the surface. The block comes to rest after travelling distance 5m. If the mass of the block is halved and velocity is doubled, the distance covered by the block before it comes to rest is,

If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane F = x i ^ + y j ^ , then:

A body is displaced from position A to position B under the influence of three forces P 1 , P 2 and P 3 . Speed of the body remains unchanged. If work done by P 1 is +180J, work done by P 2 is -80 J, then what is the work done by P 3 ?

If force is always perpendicular to motion : (i) kinetic energy remains constant (ii) work done is zero (iii) velocity is constant (iv) speed is constant

A man throws the bricks to a height of 12 m where they reach with a speed of 12 m/s, if he throws the bricks such that they just reach that height, what percent of energy will be saved? [g = 10 m/s 2 ]

Scalar product of force with velocity is called

A vehicle needs an engine of 7500 watt to keep it moving with a constant velocity of 20 m/sec on a horizontal surface. The force resisting the motion is :

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in figure, correctly shows the displacement-time curve for its motion?

A conservative force is acting on a particle. Work done by the force in displacing the particle from A to B is 90 J, from A to C is 140 J. Then the work done by the force in displacing the particle from B to C is

An electric motor creates a tension of 4500 newton in a hoisting cable and reels it in at the rate of 2 m/s, What is the power of this motor?

An engine develops 10 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m? (g = 10m/s 2 )

A body initially at rest is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to :

Total mechanical energy of a system is 24 Joule. If minimum potential energy stored in the system is 6 Joule and dissipative forces are absent, then maximum kinetic energy that the system can possess is

An electric pump is used to fill an overhead tank of capacity 9 m 3 kept at a height 10 m above ground. If the pump takes 5 minutes to fill the tank by consuming 10 kW power, efficiency of the pump should be : (take g = l0 m/s 2 )

An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that, the efficiency of engine is 60%. If g = 10 ms -2 , the power of this engine is :

A particle of mas s M starting from rest undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is :

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P 0 . The instantaneous velocity of this car is proportional to

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is :

A body of mass 1 kg begins to move under the action of a time dependent force F = 2 t i ^ + 3 t 2 j ^ N where i ^ and j ^ jare unit vectors along x and y-axis. What power will be developed by the force at the time t

A block of mass 20 kg is moved with constant velocity along an inclined plane of inclination 37° with help of a force of constant power 50 W. If the coefficient of kinetic friction between block and surface is 0.25, then what fraction of power is used against gravity?

Figure shows a body of mass M sliding from rest, down a frictionless track of radius R in time t. Assume that the body started from the top of the track A and slides to the bottom B. The change in the gravitational potential energy is:

The PE of a simple pendulum is maximum when it is :

Two springs A and B (K A = 2K B ) are stretched by same suspended weight, The ratio of work done in stretching is :

A particle of mass m is taken along different frictionless paths AB as indicated by the following diagrams. In each case, the particle starts from rest at A and reaches the point B finally. All the paths are in a vertical plane and the external forces act such that the particle moves along the respective paths without restraint; Which of the following statements will be true in respect of the above motions?

A spring of force constant 10 N/m has initial stretch 0.2 m. In changing the stretch to 0.25 m, the increase of PE is about :

Two springs have their force constants as K 1 and K 2 (K 1 > K 2 ). The work done, when both are stretched by the same amount of length, will be :

A particle is moving along a straight line under the action of a force. Its kinetic energy varies with time as KE = 7t. Force acting on the particle :

When the kinetic energy of a body is doubled, its momentum increases by . . . . . times.

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is :

Two Masses of M and 4M are moving with equal kinetic energy. The ratio of their linear momenta is :

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take ‘g’ constant with a value 10 m/s 2 . The work done by the (i) gravitational force and the (ii) resistive force of air is :

Find the compression in spring so that the block travels a distance of 8m and instantaneous come to rest after block is released?

A box of books that weighs 40 N is dragged at a speed of 1.5 m/s across a rough floor. If the coefficient of friction between the floor and the box is A.20, what is the rate at which heat energy is dissipated?

A block of mass m lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (with spring constant k)whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x = 0). When a constant horizontal force F in the positive direction of the x-axis is applied to it, a plot of the resulting kinetic energy of the block versus its position x is shown in figure. What is the magnitude F ?

KE of a body of mass m and momentum p, is given by:

A light and a heavy body have equal KE. Which one has a greater momentum?

If the KE of a body becomes. four times of its initial value, then the new momentum will be:

Which of the following is correct?

The bob of a pendulum is released from a horizontal position A as shown in the figure. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point B, given that it dissipated 5% of its initial energy against air resistance?

A body of mass 2kg has an initial speed 5ms –1 . A force acts on it for 4 seconds in the direction of motion. The force time graph is shown in figure. The final speed of the body is

A man is standing on a cart of mass double the mass of the man. Initially, the cart is at rest on the smooth ground. Now man jumps with relative velocity v horizontally towards the right with respect to cart. What will be the work done by the man during the process of jumping?

A grinding machine whose wheel has a radius of 1 π is rotating at 2.5 rev/sec. A tool to be sharpened is held against the wheel with a force of 40N. If the coefficient of friction between the tool and the wheel is 0.2, power required is

The potential energy of a spring when stretched through a distance x is 10 J. What is the amount of work done on the same spring stretch it through an additional distance T?

A force given by the relation F = 8t, acts on a body of mass 2 kg, initially at rest. Find the work done by this force on the body during first 2 seconds of its motion.

Two masses m and 2m are attached to two ends of an ideal spring and the spring is in the compressed state. The energy of spring is 60 joule. If the spring is released, then

A light spring of length l and spring constant K is placed vertically on the table. A small ball of mass m is released on it. Height from the surface of the table at which the ball will have maximum velocity

Two plates whose masses are m 1 and m 2 respectively are connected by a massless spring as shown in figure. What minimum force should be applied to the upper plate for it to lift the lower one after the force is removed.

A cricket ball is hit for a six by the bat at an angle of 45 0 to the horizontal with kinetic energy K. At the highest point, the kinetic energy of the ball is

A particle moves under the effect of a force F = c x from x = 0 to x = x 1 The work done in the process is

A body of mass m accelerates uniformly from rest to v, in time t, . As a function of t, the instantaneous power delivered to the body is

Work done in time t on a body of mass m which is accelerated from rest to a speed y in time t 1 as a function of time t is given by

A particle of mass 0 . 1kg is subjected to a force which varies with distance as shown in fig. (f). If it starts its journey from rest at x = 0, its velocity at x = 12 m is

A train weighing tO7 N is running on a level track with uniform speed of 36 km/h. The frictional force is 0 . 5 kg f per quintal. What is the power of the engine ? Take g = 10 m / s 2

The K.E. of a body decreases by 19%. What is the percentage decrease in momentum ?

The kinetic energy acquired by a mass m in traveling a certain distance d, staring from rest, under the action of a constant force is directly proportional to

A uniform chain of length I and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is

A particle is fired with speed u making angle θ with the horizontal. Its potential energy at the highest point is

A particle of mass M is moving along a circular path of consultant radius R. The centripetal acceleration varies as a a = K 2 Rt 2 , where K is constant and t is the time elapsed. What is the power delivered to the particle by the force acting on it ?

A spring is compressed between two toy carts of masses m 1 and m 2 . When the toy carts are released the spring exerts on each toy cart equal and opposite forces for the same time t. If the coefficients of friction μ between the ground and the toy carts are equal, then the displacements of the toy carts are in the ratio :

A car is moving on a straight horizontal road with a speed v. If the coefficient of friction between the tires and the road is μ , the shortest distance in which the car can be stopped is

A ball is projected vertically upwards with an initial velocity. Which of the following graphs [Fig. (3)] best represents the K.E. of the ball as a function of time from the instant of projection till it reaches back the point of projection ?

A constant force F is applied to keep the particle moving with uniform velocity v. Then the power required is

From a waterfall, water is falling down at the rate of 100 kg/s on the blades of turbine. If the height of the fall is 100 m, then the power delivered to the turbine is approximately equal to

A car of mass m is driven with acceleration a along a straight level road against a constant external resistivity force R. When the velocity of car is v, the rate at which the engine of the car is doing work will be

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electric energy. For wind speed v, the electric power output will be proportional to

A vehicle is moving on a horizontal road at a constant speed of t0 m/s. The engine needs to spend 5 k J energy per second. What is the force on the vehicle ?

A block of mass 2 kg slides down a curved track that is one quarter of a circle of radius 1 m [see fig. (1)]. Its speed at the bottom is 4 m,/s. Work done by frictional force is (take g = 10 m / s2 )

Water enters in a turbine at a speed of 700 m,/s and leave at 400 m/s If 2 × 10 3 kg / s of water flows and efficiency is 75% then output power is

A running man has half the kinetic energy that a body half his mass has. The man speeds up by f m/s and then has the same kinetic energy as the boy. The original speed of the man is

A metre stick of mass 400 gm is pivoted at one end and it is hanging freely .If the rod is displaced through an angle 60 o . The increase in its potential energy is

The spring extends by x on loading, then energy stored by the spring is If (If T is the tension in spring and ft is spring constant)

A particle of mass m 1 , is moving with a velocity v 1 and another particle of mass M 2 is moving with a velocity v 2 Both of them have the same momentum but their different kinetic energies areE 1 and E 2 respectively’ If m 1 > m 2, then

The power of water pump is 2 kW . If g =10 m /s 2 , then amount of water it can raise in 1 minute to a height of 10 m is

The upper half of an inclined plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the Lower half is given by

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 of 45 0 with the initial vertical direction is

A uniform chain of length 2 m is kept on a table such that a length of60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table ?

An engine exerts a force F = ( 20 i ^ – 3 j ^ + 5 k ^ ) N and moves with velocity v = ( 6 i ^ + 20 j ^ – 3 k ^ ) ms – 1 . The power of the engine (in watt) is

A rod of mass m and length I is lying on a horizontal table. Work done in making it stand on one end will be

The pointer reading versus load graph for a spring balance is as shown in the figure. The spring constant is

Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their momenta is

If ν , ρ and E denote velocity, linear momentum and kinetic energy of the particle respectively, then

A bicyclist comes to a skidding stop in 10m. During this process, the force on the bicycle due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is [NCERT Exemplar]

A particle is moved from (0, 0′ to ( a , a ) under a force from two paths. Path 1 is OP and path 2 is OQP . Let W 1 and W 2 be the work done by this force in these two paths. Then

An engine of one metric ton is going up an inclined plane 1 in 2 at the rate of 36 km/hr. If the coefficient of friction is (1/√3), the power of the engine in watt is

An object of mass m, initially at rest under the action, of a constant force F attains a velocity v in time t. Then, the average power supplied to mass is

How much mas:’; is converted into energy per day in Tarapur nuclear power plant operated at 10 7 kW’?

A long spring is stretched by 2 cm. Its potential energy is U . If the spring is stretched by 10 cm, its potential energy would be

The potential energy between the atoms in a molecule is given by U ( x ) = a x 12 – b x 6 where, a and b are positive constants and x is the distance between the atoms . The atom is in equilibrium when

The curved portions are smooth and horizontal surface is rough. The block is released from P . At what distance from A , it will stop (if μ = 0.8)?

A small block of mass 0⋅1 kg is pressed against a horizontal spring fixed at one end to compress the spring through 5⋅0 cm as shown in figure. The spring constant is 100 N/m. When released the block moves horizontally till it leaves the spring. Where will it hit the ground 2 m below the spring ?

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ‘t’ is proportional to

A point of application of a force F = 5 i -3 j+2 k is moved from r i -2i+7 j+4k to r 2 =-5i+ 2j+3k. The work done is

A particle moves with a velocity 6 i-4j+3k m/s under the influence of a constant force F = 20 i+ 15j -5 k newton. The instantaneous power applied to the particle is

Power supplied to a particle of mass 2 kg varies with time as P = 3 t 2 2 W . Hence, t second. If particIe is rest at t = 0, then velocity of particle at time t = 2 s will be

A block of mass 1 kg slides down a rough inclined plane of inclination 60 0 starting from its top. If coefficient of kinetic friction is 0.5 and length of the plane d = 2 m, then work done against friction is

The net work done by the tension in the figure when the bigger block of mass M touches the ground is

The force required to stretch a spring varies with the distance as shown in the figure . If the experiment is performed with the above spring of half the length, the line OA will

A motor drives a body along a straight line with a constant force. The power P developed by the motor must vary with time t as

A force F acting on a body depends on its displacement s as F ∝ s – 1 / 3 . The power delivered by F will depend on displacement as

A small block of mass m is kept on a rough inclined surface of inclination θ fixed in an elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in a time t will be

A car of mass m is accelerating on a level smooth road under the action of a single force F. The power delivered to the car is constant and equal to P. If the velocity of the car at an instant is v, then after travelling how much distance will it become double?

A force of F = 0.5 N is applied on lower block as shown in figure . The work done by lower block on upper block for a displacement of 3 m of the upper block with respect to ground is (Take, 9 = 10ms 2 )

A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the following diagrams shown in figure correctly represents the displacement-time curve for its motion? [NCERT Exemplar]

A block of mass m is pulled along a horizontal surface by applying a force at an angle θ with the horizontal. If the block travels with a uniform velocity and has a displacement d and the coefficient of friction is μ , then the work done by the applied force is

If a machine perform 4000 J output work and 1000 J is inside loss due to friction, then find the efficiency.

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k ‘ . If they are connected in parallel and force constant is k ” , then k ‘ : k ” is [NEET 2017]

Assertion : A spring of force constant k is cut into two pieces having lengths in the ratio 1 : 2. The force constant of series combination of the two parts is 3k/2. Reason : The spring connected in series are represented by k = k 1 + k 2 . [AIIMS 2017]

A force F = – k ( y i ^ + x j ^ ) where k is a positive constant, acts on a particle moving in the XY -plane. Starting from the origin, the particle is taken along the positive X-axis to the point ( a , 0) and then parallel to the Y -axis to the point ( a , a ). The total work done by the force on the particle is [AIIMS 2017]

A block of mass m = 11. 7 kg is to be pushed a distance of s = 4.65 m along an incline and raised to a distance of h = 2.86 m. Assuming frictionless surface, calculate the work done in applying a force parallel to the incline to push the block up at a constant speed. (Take, g = 9.8 ms – 2 )

A ball of mass m accelerates uniformly from rest to v 1 in time t 1 • As a function of t , the instantaneous power delivered to the body is

The kinetic energy of a body of mass 4 kg and momentum 6 N-s will be

A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time t is proportional to [Uttarakhand PMT 2014)

If a machine gun fires n bullets per second each with kinetic energy K, then the power of the machine gun is

If two persons A and B take 2 s and 4 s respectively to lift an object to the same height h, then the ratio of their powers is [Kerala CEE 2014)

A uniform force of ( 3 i ^ + j ^ ) N acts on a particle of mass 2 kg. Hence, the particle is displaced from ( 2 i + k ) m to position ( 4 i ^ + 3 j ^ – k ^ ) m The work done by the force on the particle is [NEET 2013)

The power ( P ) of an engine lifting a mass of 100 kg up to a height of 10m in 1 min is [J&K CET 2013)

A body of mass 300 kg is moved through 10m along a smooth inclined plane of angle 30 0 . The work done in moving (in joules) is (Take, g = 9.8 ms -2 )

Force constants of two wires A and B of the same material are k and 2k, respectively. If the two wires are stretched equally, then the ratio of work done in stretching W A W B is

Two masses m and 2m are attached to two ends of an ideal spring as’ shown in figure. When the spring is in the compressed state, the energy of the spring is 60J, if the spring is released, then at it:- natural length, [BHU 2012]

A string of length L and force constant k is stretched to obtain extension l . It is further stretched to obtain extension l 1 . The work done in second stretching is [MHT CET 2014]

A load suspended by a massless spring produces an extension of x cm in equilibrium. When it is cut into two unequal parts, the same load produces an extension of 7.5 cm when suspended by the larger part of length 60 cm. When it is suspended by the smaller part, the extension is 5.0 cm. Then,

A smooth curved surface of height 10m is ended horizontally. A spring of force constant 200 Nm – 1 is fixed at the horizontal end as shown in figure. When an object of mass 10 g is released from the top, it travels along the curved path and collides with the spring. Then, the maximum compression in the spring is (Take, g = 10 ms – 2 )

A force F = ( 6i −8 j ) N, acts on a particle and displaces it over 4 m along the X-axis and then displaces it over 6 m along the Y-axis. The total work done during the two displacements is

A man weighing 80 kg climbs a staircase carrying a 20 kg load. The staircase has 40 steps each of 25 cm height. If he takes 20 seconds to climb, the work done is…..joule

A body of mass 5 kg is moved up over 10 m along the line of greatest slope of a smooth inclined plane of inclination of 30° with the horizontal. If g=10m/s 2 , the work done will be in joule is ……….

A bucket of mass ‘m’ tied to a light rope is lowered at a constant acceleration of ‘g/4’. If the bucket is lowered by a distance ‘d’, the work done by the rope will be (neglect the mass of the rope)

A lorry and a car moving with same momentum are brought to rest by applying the same retarding force. Then

A car of mass ‘m’ is driven on a surface with an accelaration ‘a’. Frictional force on the car is ‘x’. At an instant the velocity of car is ‘v’, the power of engine is

A motor pump set of efficiency 80%, lifts 800 litres of water in 19.6 seconds over a head of 20 m. Its input power is

A simple pendulum bob has a mass “m” and length “L”. The bob is drawn aside such that the string is horizontal and then it is released. The velocity of the bob while it crosses the equilibrium position is

A motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver n-times the water through the same pipe in the same time the power of the motor must be increased as follows.

A block of mass ‘m’ is connected to one end of a spring of ‘spring constant’ k. The other end of the spring is fixed to a rigid support. The mass is released slowly so that the total energy of the system is then constituted by only the potential energy, then ‘d’ is the maximum extension of the spring. Instead, if the mass is released suddenly from the same initial position, the maximum extension of the spring now is ( g is acceleration due to gravity )

A lifting machine, having an efficiency of 80% uses 2500 J of energy in lifting a 10 kg load over a certain height. If the load is now allowed to fall through that height freely, its velocity at the end of the fall will be (take acceleration due to gravity as 10 m/s2 )…….ms -1

Two identical blocks A and B, each of mass ‘m’ resting on smooth floor are connected by a light spring of natural length L and the spring constant K, with the spring at its natural length. A third identical block C (mass m) moving with a speed v along the line joining A and B collides with A. The maximum compression in the spring is………….

A force F acting on a body depends on its displacement s as F α S – 1 3 . The power delivered by F will depend on displacement as

The potential energy of a particle in a force filed is u = A r 2 – B r where A and B are positive constants and ‘r’ is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle

A ladder 2.5 m long and 150 N weight has its center of gravity 1 m from one end. At the other end 40 N load is attached. The whole system is horizontal. The work to be done to keep the ladder in vertical position so that the load is at the top end is ………joule

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