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. `5 g//6`
B. `g`
C. `2g//3`
D. `g//2`

Answer

D

Explanation

If `a` is acceleration of mass on release, then as is clear from Fig.
`ma = mg - T` ..(i)
For the cylinder,
Torque `= T xx R = I alpha = mR^(2).((a)/(R ))`
`:. T = ma`
From (i), `ma = mg - ma`
`2ma = mg or a = g//2`