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Q.
For the given uniform square lamina $A B C D$, whose centre is $O$
System of Particles and Rotational Motion
Solution:
Let $I$ be the moment of inertia of the square lamina
about an axis through $O$ and perpendicular to its plane. Then by
perpendicular axes theorem, $I_{A C}+I_{B D}=I$
$\text { or } I_{A C}=\frac{I}{2} \quad\left[\because I_{A C}=I_{B D}\right]$
Again by perpendicular axes theorem,
$I_{E F}+I_{G H}=I$
or $I_{E F}=\frac{I}{2} \left[\because I_{E F}=I_{G H}\right]$
Hence $I_{A C}=I_{F F}$
