Work, Energy and Power

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