A mass m supported by a massless string wound around a uniform hollow cylinder of mass m and radius R…

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?

Numerical

(a)2g/3

(b)g/2

(c)5g/6

(d)g

Ans: (b)

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