Q. Consider a uniform square of this 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) ${5/6\ ma}^{2}$
B) ${1/12\ ma}^{2}$
C) ${7/12\ ma}^{2}$
D) ${2/3\ ma}^{2}$
Explanation
(d) Moment of inertia of square plate about $XY\ is\frac{ma^{2}}{6}$
Moment of inertia about $ZZ''$ can be computed using
parallel axis theorem
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$I_{ZZ^{''}} = I_{XY} + m\left( \frac{a}{\sqrt{2}} \right)^{2}$
$= \frac{ma^{2}}{6} + \frac{ma^{2}}{2} = \frac{2ma^{2}}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.