Question

A plank with a uniform sphere placed on it rests on a smooth horizontal plane. Plank is pulled to right by a constant force F. If sphere does not slip over the plank, which of the following is correct ?

• A. Acceleration of the centre of sphere is less than that of the plank.
• B. Work done by friction acting on the sphere is equal to its total kinetic energy
• C. Total kinetic energy of the system is is equal to work done by the force F.
• D. None of the above.

Answer 1

Answer: (A), (B), (C)

The correct options are
A Work done by friction acting on the sphere is equal to its total kinetic energy
B Acceleration of the centre of sphere is less than that of the plank.
C Total kinetic energy of the system is is equal to work done by the force F.

Due to the force F, the plank has the tendency to slide to the right. Hence friction acts on the plank to the left and on the sphere to the right. Thus the friction acts on the accelerating force on the sphere and also produces an anticlockwise moment. Therefore, the sphere experiences a rightward translational acceleration and an anti clockwise angular acceleration at once. If angular acceleration of the sphere is $\alpha$ then its center of mass has backward acceleration $r\alpha$ relative to the plank. Hence, its net acceleration becomes more than that of plank. Thus A is correct.
Since there is no sliding between the surfaces of the sphere and the plank, no energy is lost against friction. Since friction acting on the sphere is the only force which provides motion to it, thus KE of the sphere at any instant is equal to work done by the friction acting on it. Hence option B is correct.
Since no energy is lost against friction thus KE of the whole system is equal to work done by the force F. Hence option C is also correct.