First slide

Rolling motion

Question

A ball is released from the top (A) of a semi cylindrical surface of which part AB is sufficiently rough and BC is smooth. Then:

Moderate

A

The maximum angular velocity of the ball will be at point B only
B

The maximum speed of centre of the ball will not be at point B
C

Ball will never reach point C
D

Ball may reach point C if friction is not sufficient to provide pure rolling

Solution

Section AB is smooth, so the initial potential energy will convert into only translational kinetic energy. After point B, due to rough surface, some energy will also convert into rotational kinetic energy . Thus, it cannot reach to point C.

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