Find the MOI of a uniform square plate of mass $m$ and edge $a$ about one of its diagonals.

\frac{M a^{2}}{6}

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\frac{M a^{2}}{3}

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\frac{M a^{2}}{9}

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\frac{M a^{2}}{12}

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Solution

The correct option is D $\frac{M a^{2}}{12}$
Using perpendicular axis theorem,
$I_{z} = I_{x} + I_{y} = I_{1} + I_{2} = 2 I_{x} = 2 I_{1}$
$I_{1} = I_{x}$
Moment of inertia about diagonal is
$∴ I_{1} = \frac{M a^{2}}{12}$

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