A plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the right by a constant force `F`. It the sphere does not slip over the plank, then

Options

A. both have the same acceleration
B. acceleration of the centre of sphere is less than that of the plank
C. work done by friction acting on the sphere is equal to its total kinetic energy
D. total kinetic energy of the system is equal to work done by the force `F`

Answer

B, C, D

Explanation

Due to force `F` the plank has a tendency to slide to the right below the sphere. Hence, friction acts on the plank to the left and that on the sphere acts to the right. The friction not only acts that on the sphere acts to the right. The friction not only acts on accelerating force on the sphere but also produces an anticlocwise moment. Therefore, the sphere experiences a righward translational acceleration and an anticlockwise angular acceleration simltaneously.
If the angular acceleration of the sphere is `alpha` then its centre of mass has a backward acceleration `ralpha` relative to the plank. Hence, its net acceleration becomes less than that of the plank. Hence, option b is correct. obviously option a is incorrect.
Since there is no sliding between the surfaces of the sphere and the plank, therefore, no energy is lost against friction.
Since friction, acting on the sphere, is the only force which provides motion to it, therefore `KE` of the sphere at any instant is equal to work done by the friction acting on it. Hence, option c is correct.
Since no energy is lost against friction therefore `KE` of the whole system is equal to work done by force `F`. Hence, option d is also correct.