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  4. 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?

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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?Physics Question Image

AIPMTAIPMT 1999System of Particles and Rotational Motion

Solution:

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.