Question

A mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, then with what acceleration will the mass release?
(Assume $g$ = acceleration due to gravity)

• A. $\frac{2 g}{3}$
• B. $\frac{g}{2}$
• C. $\frac{5 g}{6}$
• D. $g$

Answer 1

Answer: (B)

The given situation is shown in the following figure

Initial torque on cylinder due to force of mass $m$ is $\tau=F R=m g R$
If $\alpha$ is angular acceleration of cylinder, then $\tau=I \alpha$
where, $I=$ moment of inertia $=m R^{2}$
$\alpha=\frac{\tau}{I}=\frac{m g R}{m R^{2}} $
$\Rightarrow \alpha=\frac{g}{R}$
As linear acceleration,
$a=R \alpha=R \cdot \frac{g}{R}=g$