Question

A block $A$ starts sliding on a smooth track from a height $h$ as shown in the figure. The track smoothly joins into a conveyor belt which is being driven by a pulley of radius $r$ . If the angular velocity $\omega $ of the pulley is such that the block $A$ doesn't slip on the belt, then the value of $\omega $ is

• A. $\frac{\sqrt{g h}}{r}$
• B. $\frac{\sqrt{g h}}{2 r}$
• C. $\frac{\sqrt{2 g h}}{r}$
• D. $\frac{2 \sqrt{g h}}{r}$

Answer 1

Answer: (C)

The speed of the block on reaching the conveyor belt is
$v=\sqrt{2 g h}$
There will be no slipping between the block and the belt if both have the same linear velocity.
$\Rightarrow v=\sqrt{2 g h}=\omega r\Rightarrow \omega =\frac{\sqrt{2 g h}}{r}$