Physics - Rotation Question with Solution | TestHub

The distance of each point mass from the center of the square is half the length of the diagonal. The diagonal length is $L\sqrt{2}$. So, the distance $r$ for each mass is $r=\frac{L\sqrt{2}}{2}=\frac{L}{\sqrt{2}}$. The moment of inertia of one point mass is $m{r}^2=m{\left(\frac{L}{\sqrt{2}}\right)}^2=m\frac{L^2}{2}$. Since there are four such masses, the total moment of inertia is $$I_{total}=4\times m\frac{L^2}{2}=2m{L}^2$$.