Q 11-06-018JEE MainAIEEE 2008Easy
Consider a uniform square plate of side $a$ and mass $m$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
Answer: (D) $\dfrac{2}{3}ma^2$
About the perpendicular axis through the centre: $I_c = \dfrac{m(a^2 + a^2)}{12} = \dfrac{ma^2}{6}$.
The corner is $\dfrac{a}{\sqrt{2}}$ from the centre. Parallel axis theorem:
$$I = \frac{ma^2}{6} + m\cdot\frac{a^2}{2} = \frac{2}{3}ma^2$$
Solution by Sreeraj P, M.Sc Physics