Question

A disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$, is

• A. $\sqrt{2 g h}$
• B. $\sqrt{\frac{2}{3} g h}$
• C. $2 \sqrt{\frac{g h}{3}}$
• D. $\frac{1}{2} \sqrt{3 g h}$

Answer 1

Answer: (C)

Using Mechanical energy conservation
$m g h=\frac{1}{2} m v^{2}+\frac{1}{2}\left(\frac{1}{2}\right) m r^{2} \cdot \frac{v^{2}}{r^{2}}$
$m g h=\frac{3}{4} m v^{2}$
$v^{2}=\frac{4 g h}{3}$
$v=\sqrt{\frac{4 g h}{3}}$