Q 11-06-017JEE MainAIEEE 2007Medium
For the given uniform square lamina ABCD, whose centre is O, E and F are the midpoints of AB and DC. Then
Answer: (C) $I_{AC} = I_{EF}$
Concept. For a square lamina, by symmetry and the perpendicular-axis theorem, every axis in its plane through the centre has the same moment of inertia, $\tfrac1{12}Ma^2$.
Step 1. Why. $I_z=I_{EF}+I_{\perp EF}=2I_{EF}$ and also $I_z=I_{AC}+I_{BD}=2I_{AC}$ (each pair is perpendicular and equal by symmetry). So $I_{AC}=I_{EF}$.
Answer. Option C.
Solution by Sreeraj P, M.Sc Physics
