Work, Energy and Power · Question 16

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