Question

A mass ${}^{\prime }{m}^{\prime }$ 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, with what acceleration will the mass fall on release ?

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

Answer 1

The correct option is D $\frac{g}{2}$

Let us suppose acceleration of mass is $a$.
According to question -


Applying $\sum F=\text{ma}$ for mass:
$mg-T=ma....\left(1\right)$
Applying $\sum \tau =I\alpha$ for hollow cylinder:
$T.R=m{R}^2\frac{a}{R}....\left(2\right)$
$T=ma....\left(2\right)$
On adding (1) and (2)

$\frac{g}{2}=a$