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Q.

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?

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a

$\frac{2 g}{3}$

b

$\frac{g}{2}$

c

g

d

$\frac{5 g}{6}$

answer is A.

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Detailed Solution

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Question Image

For block $T = mg - ma$

For hollow cylinder $I α = T \times R$
here $a = R α$

$\frac{{mR}^{2}}{2} \times \frac{a}{R} = (mg - ma) R \Rightarrow a = \frac{2 g}{3}$

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