Question

A mass m 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 with the mass fall on release?

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

Answer 1

The correct option is D

$\frac{g}{2}$

For mass m, $mg-T=ma$
For no slipping, $a=\alpha R$
For the pulley, $TR=m{R}^2\alpha$
Solving we get $a=\frac{g}{2}$