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In the rectangular lamina A B C D shown in Fig, $a = A B = B C / 2$ . The moment of inertia of the lamina is the minimum along the axis passing through

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Detailed Solution

$I_{BC} = \frac{m (A B)^{2}}{3} = \frac{m a^{2}}{3} I_{AB} = \frac{m (B C)^{2}}{3} = \frac{4}{3} m a^{2} I_{HF} = \frac{m (A B)^{2}}{12} = \frac{m a^{2}}{12} I_{EG} = \frac{m (B C)^{2}}{12} = \frac{m a^{2}}{3}$

Thus, the moment of inertia about HF is the minimum.

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