Work, Energy and Power

The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s is : (g = 9.8 m/s2)

1. 19.6 kW
2. 19.6 W
3. 39.2 kW
4. 39.2 W

Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of length 10 m, as shown in the figure. Point mass A of mass m travelling horizontally with speed 10 ms-1 hits bob B elastically. The bob B rises h meter after the collision. Taking the acceleration due to gravity g = 10 ms-2 and neglecting the size of the bob, the value of h is: [figure]

1. 2.5
2. 8
3. 7
4. 5

A particle of mass M moves along a horizontal x axis from x = 0 to x = L. The coefficient of kinetic friction varies as a function of x as k(x) = 0 - x, where 0, are constants of appropriate dimensions, so that k(L) = 0. The total work done by the frictional force during the motion is n 0MgL, where g is the acceleration due to gravity. The value of n is:

1. 12
2. 3
3. 1
4. 13

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If FA and FB are the forces applied by the brakes on cars A and B respectively, then the ratio of FAFB is

1. 13
2. 12
3. 32
4. 23

A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity v0 as shown in figure. If the string gets slack at some point P making an angle from the horizontal, the ratio of the speed v of the bob at point P to its initial speed v0 is: [figure]

1. ( 2 + 3 ) 12
2. ( 2 + 3 ) 12
3. ( ) 12
4. ( 12 + 3 ) 12

At any instant of time t, the displacement of any particle is given by 2t - 1 (SI unit) under the influence of force of 5 N. The value of instantaneous power is (in SI unit):

1. 10
2. 5
3. 7
4. 6

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v1 while body B is at rest before collision. The velocity of the system after collision is v2. The ratio v1 : v2 is

1. 1 : 2
2. 2 : 1
3. 4 : 1
4. 1 : 4

An object moving along horizontal x-direction with kinetic energy 10 J is displaced through x = (3 i) m by the force F = (-2 i + 3 j) N. The kinetic energy of the object at the end of the displacement x is

1. 10 J
2. 16 J
3. 4 J
4. 6 J

An object falls from a height of 10 m above the ground. After striking the ground it loses 50\% of its kinetic energy. The height upto which the object can rebound from the ground is:

1. 7.5 m
2. 10 m
3. 2.5 m
4. 5 m

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

1. 4U
2. 8U
3. 16U
4. 2U

An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 ms-1. The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is : (g = 10 ms-2)

1. 23000
2. 20000
3. 34500
4. 23500

A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively -

1. S4, 3gS2
2. S4, 3gS2
3. S4, 3gS2
4. S2, 3gS2

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10\% of the input energy. How much power is generated by the turbine? (g = 10 m/s2)

1. 7.0 kW
2. 10.2 kW
3. 8.1 kW
4. 12.3 kW

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 :

1. 5 J
2. 25 J
3. 20 J
4. 30 J

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when :

1. the wire is horizontal
2. inclined at an angle of 60 from vertical
3. the mass is at the lowest point
4. the mass is at the highest point

Body A of mass 4m moving with speed u collides with another body B of mass 2 m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :

1. 59
2. 49
3. 89
4. 19

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

1. 0.5
2. 0.25
3. 0.8
4. 0.4

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to [figure]

1. D
2. 32D
3. 75D
4. 54D

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

1. (i) 1.25 J (ii) -8.25 J
2. (i) 100 J (ii) 8.75 J
3. (i) 10 J (ii) -8.75 J
4. (i) -10 J (ii) -8.25 J

A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t2 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?

1. (2t3 + 3t4) W
2. (2t3 + 3t5) W
3. (2t2 + 3t3) W
4. (2t2 + 4t4) W

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

1. 3gR
2. 5gR
3. gR
4. 2gR

Two identical balls A and B having velocities of 0.5 m s-1 and -0.3 m s-1 respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be :

1. -0.5 m s-1 and 0.3 m s-1
2. 0.5 m s-1 and -0.3 m s-1
3. -0.3 m s-1 and 0.5 m s-1
4. 0.3 m s-1 and 0.5 m s-1

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 ?

1. 8 J
2. 11 J
3. 5 J
4. 2 J

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is (Take g = 10 m s-2)

1. 28 m s-1
2. 10 m s-1
3. 14 m s-1
4. 20 m s-1

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle to its initial direction and has a speed v3. The second block's speed after the collision is

1. 3 2v
2. 32v
3. 2 23v
4. 34v

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

1. 2mk t-1/2
2. 12 mk t-1/2
3. mk2 t-1/2
4. mk t-1/2

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 = 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be

1. 275 J
2. 250 J
3. 475 J
4. 450 J

Two particles of masses m1, m2 move with initial velocities u1 and u2. On collision, one of the particles gets excited to higher level, after absorbing energy . If final velocities of particles be v1 and v2 then we must have :

1. 12m1u12 + 12m2u22 - = 12m1v12 + 12m2v22
2. 12m12u12 + 12m22u22 + = 12m12v12 + 12m22v22
3. m12u1 + m22u2 - = m12v1 + m22v2
4. 12m1u12 + 12m2u22 = 12m1v12 + 12m2v22 -

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

1. WP > WQ; WQ > WP
2. WP < WQ; WQ < WP
3. WP = WQ; WP > WQ
4. WP = WQ; WP = WQ

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

1. = 2
2. =
3. = 1
4. = 2