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Q.

The moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its center of gravity and perpendicular to its length. The relation between its length $L$ and radius $R$ is

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a

$L = \sqrt{2} R$

b

$L = R$

c

$L = \sqrt{3} R$

d

$L = 3 R$

answer is B.

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Detailed Solution

$\frac{M L^{2}}{12} + \frac{M R^{2}}{4} = \frac{M R^{2}}{2} \Rightarrow \frac{L^{2}}{12} = \frac{R^{2}}{4} \Rightarrow L = \sqrt{3} R$

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