Q. A thin uniform square lamina of side $a$ is placed in the $xy$-plane with its sides parallel to $x$ and $y$-axis and with its centre coinciding with origin. Its moment of inertia about an axis passing through a point on the $y$-axis at a distance $y = 2a$ and parallel to $x$-axis is equal to its moment of inertia about an axis passing through a point on the $x$-axis at a distance $x = d\ $and perpendicular to $xy$-plane. Then value of $d$ is
A) $\frac{7}{3}a$
B) $\sqrt{\frac{47}{12}a}$
C) $\frac{9}{5}a$
D) $\sqrt{\frac{51}{12}a}$
Explanation
(b) $\frac{ma^{2}}{12} + m\left( 4a^{2} \right) = \frac{ma^{2}}{6} + md^{2}$
or $d^{2} = \frac{47a^{2}}{12}$
$\therefore$ $d = \sqrt{\frac{47}{12}}\ a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.