Question

$I$ is the moment of inertia of a thin square plate about an axis passing through opposite corners of plate. The moment of inertia of same plate about an axis perpendicular to the plane of plate and passing through its centre is :

• A. $\frac{I}{2}$
• B. $\frac{I}{\sqrt{2}}$
• C. $\sqrt{2}I$
• D. $2I$

Answer 1

The correct option is D $2I$

By perpendicular axis theorem

$I_O=I_{AC}+I_{BD}$

By symmetry, $I_{AC}=I_{BD}=I$

$\therefore I_O=2I$