A thin uniform square lamina of side $a$ is placed in the $x y$-plane with its sides parallel to $X$ and $Y$-axes 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 $Y=2 a$ and parallel to $X$-axis is equal to its…

Question

A thin uniform square lamina of side $a$ is placed in the $x y$-plane with its sides parallel to $X$ and $Y$-axes 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 $Y=2 a$ 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 $x y$-plane. Then value of $d$ is

Aicharya · Accepted Answer

$\begin{array}{rlrl}\frac{m a^2}{12}+m\left(4 a^2ight) & =\frac{m a^2}{6}+m d^2 \ & 	ext { or } \quad d^2 & =\frac{47 a^2}{12} \ 	herefore & d & =\sqrt{\frac{47}{12}} a\end{array}$

A thin uniform square lamina of side $a$ is placed in the $x y$-plane with its sides parallel to $X$ and…

Solution