Question

The moment of inertia of a uniform square plate of mass $M$ and edge $a$ about one of its diagonals is $\frac{M{a}^2}{x}$. Find the value of $x$.

Answer 1

$I_1=I_2$
$I_1+I_2=I_3=\frac{M{a}^2}{6}$
$\therefore 2I_1$ or $2I_2=\frac{M{a}^2}{6}$
$\therefore I_1=I_2=\frac{M{a}^2}{12}$
$\Rightarrow x=12$