Question

A sphere S rolls without slipping, moving with a constant speed on a plank P. The friction between the upper surface of P and the sphere is sufficient to prevent slipping, while the lower surface of P is smooth and rests on the ground. Initially, P is fixed to the ground by a pin N. If N is suddenly removed:

• A. S will begin to slip on P.
• B. P will begin to move backwards.
• C. the speed of S will decrease and its angular velocity will increase.
• D. there will be no change in the motion of S and P will still be at rest.

Answer 1

The correct option is D there will be no change in the motion of S and P will still be at rest.

As the body is rolling without slipping at a constant speed, it is a state of pure rolling and there is no relative motion between the bottom most point of the sphere and the plank. Thus there will be no change in the motion of S, and P ,it will still be at rest.