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. $\frac{2g}{3}$
• B. $\frac{g}{2}$
• C. $\frac{5g}{6}$
• 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 $\tau =FR=mgR$
If $\alpha$ is angular acceleration of cylinder, then $\tau =I\alpha$
where, $I=$ moment of inertia $=m{R}^2$
$\alpha =\frac{\tau }{I}=\frac{mgR}{m{R}^2}$
$\Rightarrow \alpha =\frac{g}{R}$
As linear acceleration,
$a=R\alpha =R\cdot \frac{g}{R}=g$