Question

The moment of inertia of a hollow cubical box of mass $M$ and side length $a$ , about an axis passing through centres of two opposite faces, is equal to $\frac{x M a^{2}}{18}$ . The value of $x$ is

Answer 1

Let $m$ be the mass of each face of the cubical box.
$I=2\times \left(\frac{m a^{2}}{6}\right)+4\times \left[\frac{m a^{2}}{12} + m \left(\frac{a}{2}\right)^{2}\right]$
$=\frac{5 m a^{2}}{3}$
But, $m=\frac{M}{6}$
$\therefore I=\frac{5 M a^{2}}{18}$
$\Rightarrow x=5$