Question

A block of mass $m$ is attached to one end of a light string which is wrapped on a disc of mass $2m$ and radius $R$ . The total length of the slack portion of the string is $l$ . The block is released from rest. The angular velocity of the disc just after the string becomes taut is

• A. $\sqrt{\frac{gl}{R^{2}}}$
• B. $\sqrt{\frac{gl}{2R^{2}}}$
• C. $\sqrt{\frac{2gl}{3R^{2}}}$
• D. $\sqrt{\frac{3gl}{2R^{2}}}$

Answer 1

Answer: (B)

Using the principle of conservation of angular momentum,
$m\sqrt{2 gl}\times R=\left[\frac{\left(2 m\right) \, R^{2}}{2} + \left(mR\right)^{2}\right]\times \omega $
$\Rightarrow \omega =\sqrt{\frac{gl}{2 R^{2}}}$