Question

A disc of mass $m$ and radius $r$ is free to rotate about its centre shown in the figure. A string id 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. $\sqrt{2gh}$
• B. $\sqrt{\frac{2}{3}gh}$
• C. $2\sqrt{\frac{gh}{3}}$
• D. $\frac{1}{2}\sqrt{3gh}$

Answer 1

The correct option is C $2\sqrt{\frac{gh}{3}}$

According to energy conservation,

$mgh=\frac{1}{2}m{v}^2+\frac{1}{2}I{w}^2$

we know,

$v=R\omega$

$mgh=\frac{1}{2}m{v}^2+\frac{1}{2}I{\left(\frac{v}{r}\right)}^2$

$I=\frac{1}{2}m{R}^2$

$v=\sqrt{\frac{4gh}{3}}=2\sqrt{\frac{gh}{3}}$