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Q.

Two thin rods, each of mass $m$ and length $l$ are joined to form $L$ shape as shown. The moment of inertia of rods about an axis passing through free end $(O)$ of a rod end and perpendicular to both the ends is

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a

$m l^{2}$

b

$\frac{1}{6} m l^{2}$

c

$\frac{2}{7} m l^{2}$

d

$\frac{5}{3} m l^{2}$

answer is C.

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Detailed Solution

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$d = \sqrt{l^{2} + {(l / 2)}^{2}} I = \frac{m l^{2}}{3} + [\frac{m l^{2}}{12} + m d^{2}] = \frac{5 m l^{2}}{3}$

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