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  4. The moment of inertia of a uniform square plate of mass M and edge length a about one of its diagonals is

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Q. The moment of inertia of a uniform square plate of mass $M$ and edge length a about one of its diagonals is

Solution:

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$l_{Z} = \frac{Ma^{2}}{6} $
By symmetry
$ l_{x} = l_{y} = l $
$ l_{x} = l_{y} = l_{z} $
$2l = \frac{Ma^{2}}{6} $
$ l = \frac{Ma^{2}}{12}$