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 or release?

Options

A. (a) `(2g)/(3)`
B. (b) `g/2`
C. (c) `(5g)/(6)`
D. (d) g

Answer

B

Explanation

From figure,
Acceleration `a=Ralpha` …(i)
and `mg-T=ma` …(ii)
From equation (i) and (ii)
`TxxR=mR^a=mR^2(a/R)`
or `T=ma`
`implies mg-ma=ma`
`implies a=g/2`