Work, Energy and Power

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = x, where is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be :

1. m2 2 d
2. md2 2
3. m 2 d2
4. 2m 2 d

A force (3x2 + 2x - 5) N displaces a body from x = 2 m to x = 4 m. Work done by this force is J.

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

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

[figure] A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

1. 6 m
2. 5 m
3. 1 m
4. 2 m

A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is :

1. 44\%
2. 16\%
3. 84\%
4. 32\%

Four particles A, B, C, D of mass m2, m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is :

1. B
2. C
3. D
4. A

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

1. 60%
2. 500%
3. 6%
4. 600%

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be : [figure]

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

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

1. t2/3
2. t3/2
3. t
4. t2

If a rubber ball falls from a height h and rebounds upto the height of h/2. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are :

1. 50\%, 2gh
2. 50\%, gh
3. 50\%, gh2
4. 40\%, 2gh