Work, Energy and Power · Question 34

The potential energy of a particle in a force field is U = Ar2 - Br 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 is

1. B2A
2. 2AB
3. AB
4. BA

Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction:

1. same as that of B
2. opposite to that of B
3. = -1 ( 12 ) to the x-axis
4. = -1 (- 12 ) to the x-axis

A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) with velocity 2v. The final velocity of the combination is

1. 32v i + 14v j
2. 14v i + 32v j
3. 13v i + 23v j
4. 23v i + 13v j

The potential energy of a system increases if work is done

1. upon the system by a nonconservative force
2. by the system against a conservative force.
3. by the system against a nonconservative force.
4. upon the system by a conservative force.

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

1. at the highest position of the body
2. at the instant just before the body hits the earth.
3. it remains constant all through.
4. at the instant just after the body is projected.

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

1. 18 J
2. 21 J
3. 26 J
4. 13 J

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

1. MV2T
2. 12 MV2T2
3. MV2T2
4. 12 MV2T

A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be

1. 0, 1
2. 1, 1
3. 1, 0.5
4. 0, 2

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?

1. 400 W
2. 200 W
3. 100 W
4. 800 W

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

1. 2Mg/k
2. 4Mg/k
3. Mg/2k
4. Mg/k