Q: 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 will the mass fall on release?
Sol: Applying Laws of Motion
$\large mg-T = ma$
$\large mg-T = m (R \alpha)$ …(i)
Taking Torque about centre of pulley
$\large T\times R = mR^2 \alpha$ …(ii)
Solving (i) & (ii)
a = g/2