Q. 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
A) $\frac{1}{12}\ ma^{2}$
B) $\frac{7}{12}\ ma^{2}$
C) $\frac{2}{3}\ ma^{2}$
D) $\frac{5}{6}\ ma^{2}$
Explanation
(c) M.I. of the plate about an axis perpendicular to its plane and passing through its centre
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$I_{0} = \frac{ma^{2}}{6}$
By parallel axes theorem
$I_{A} = I_{0} + m\left( \frac{a}{\sqrt{2}} \right)^{2} = \frac{2}{3}ma^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.