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 will the mass fall on release?

• A. 2g/3
• B. g/2
• C. 5g/6
• D. g

Answer 1

Answer: (B)

g/2

Answer 2

For the mass m, $mg-T=ma$
As we know, $a=R \alpha$
So, $mg-T=mR\alpha$ .....(i)
Torque about centre of pully
$T x R = mR^2\alpha$ .....(ii)
From Eqs. (i) and (ii), we get, $a=g/2$
Hence, the acceleration with the mass of a body fall is g/2.