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Q.

A mass M is supported by a massless string wound round a uniform cylinder of mass M and radius E as shown in fig. On releasing the mass from rest, it
wiII fall with acceleration

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a

g /3

b

g /2

c

g

d

2g/ 3

answer is D.

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Detailed Solution

$Mgh = \frac{1}{2} {Mv}^{2} + \frac{1}{2} {Iω}^{2}$
$\begin{array}{l} = \frac{1}{2} {Mv}^{2} + \frac{1}{2} [\frac{1}{2} {MR}^{2}] ω^{2} \\ = \frac{1}{2} {Mv}^{2} + \frac{1}{4} {Mv}^{2} = \frac{3}{4} {Mv}^{2} \\ v = \sqrt{2 ah} \\ ∴ Mgh = \frac{3}{4} M \times 2 ah \\ a = \frac{2}{3} g \end{array}$

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A mass M is supported by a massless string wound round a uniform cylinder of mass M and radius E as shown in fig. On releasing the mass from rest, itwiII fall with acceleration