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Question

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 on release?

A
5g6
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B
g
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C
2g3
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D
g2
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Solution

The correct option is D g2
Applying Newton's second law on hanging block mg - T = ma (i)
Torque on cylinder due to tension in string about center of pulley

T×R=Iα
T×R=mR2α
( I=mR2 for hollow cylinder)
T=mRα (ii)
As string is not slipping over pulley.
a=Rα (iii)
From eqns (ii) and (iii)
T = ma (iv)
From eqns (i) and (iv)
mg = 2ma
a=g2

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