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 $\frac{g}{2}$

Applying Newton's second law on hanging block mg - T = ma (i)
Torque on cylinder due to tension in string about center of pulley

$T\times R=I\alpha$
$T\times R=m{R}^2\alpha$
($\because I=m{R}^2$ for hollow cylinder)
$\Rightarrow T=mR\alpha$ (ii)
As string is not slipping over pulley.
$a=R\alpha$ (iii)
From eqns (ii) and (iii)
$\Rightarrow$ T = ma (iv)
From eqns (i) and (iv)
mg = 2ma
$\Rightarrow a=\frac{g}{2}$