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 $\frac{xM{a}^2}{18}$ . The value of $x$ is

Answer 1

Answer: 5

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