Work, Energy and Power

A uniform force of (3 i + j) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position (2 i + k) metre to position (4 i + 3 j - k) metre. The work done by the force on the particle is

1. 13 J
2. 15 J
3. 9 J
4. 6 J

A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when

1. U(x) < E
2. U(x) = 0
3. U(x) E
4. U(x) > E

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio

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

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to

1. t2P0
2. t1/2
3. t-1/2
4. t m

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