Question

A small ring is rolling without slipping on the circumference of a large bowl as shown in the figure. The ring is moving down at $P_1$, comes down to the lower most point $P_2$ and is climbing up at $P_3$. Let $\overrightarrow{v}$CM denote the velocity of the centre of mass of the ring. Choose the correct statement regarding the frictional force on the ring.

• A. It is opposite to $\overrightarrow{v}CM$ at the points $P_1,P_2$ and $P_3$
• B. It is opposite to $\overrightarrow{v}CM$ at $P_1$, and in the same direction as $\overrightarrow{v}CM$ at $P_3$
• C. It is in the same direction as $\overrightarrow{v}CM$ at $P_1$, and opposite to $\overrightarrow{v}CM$ at $P_3$.
• D. It is zero at the points $P_1,P_2$ and $P_3$

Answer 1

Answer: (B)

It is opposite to $\overrightarrow{v}CM$ at $P_1$, and in the same direction as $\overrightarrow{v}CM$ at $P_3$

As the ring is rolling without slipping, $v=R\omega$

In this scenario, the direction of friction will be against the net external force parallel to ${\overrightarrow{v}}_{CM}$.

Hence, at $P_1$, friction is directed upwards along the plane i.e. opposite to the direction of $v_{CM}$.

By same logic, At $P_3$, friction is directed upwards along the plane, i.e. in the same direction as $v_{CM}$.