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, with what acceleration will the mass fall on release?

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

Answer 1

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

$a=R\alpha$ (no slipping)

Also, $\tau =I\alpha$ and $\tau =TR$

Using the relations, $⟹T=\frac{Ia}{R^2}$

For hollow cylinder, $I=m{R}^2⟹T=ma$

Now for block, $ma=mg-T$

$ma=mg-ma$

$⟹a=\frac{g}{2}$