A square lamina is as shown in the figure. The moment of inertia of the frame about the three axes shown in the figure are $I_{1}, I_{2}$ and $I_{3}$ respectively. Select the correct alternative.

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$I_{2} = I_{3} > I_{1}$

$I_{1} > I_{2} > I_{3}$

$I_{1} < I_{2} < I_{3}$

$I_{2} = I_{3} < I_{1}$

answer is C.

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Detailed Solution

For square lamina $I_{2} = I_{3} = \frac{M L^{2}}{12}$ (Perpendicular axes theorem). This value will be less than $I_{1} = \frac{M L^{2}}{3} (\frac{M L^{2}}{12} + \frac{M L^{2}}{4})$ (parallel axis theorem).

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