Q. Four point masses, each of value $m$, are placed at the corners of a square $A B C D$ of side $l$. The moment of inertia of this system about an axis through $A$ and parallel to $B D$ is
System of Particles and Rotational Motion
Solution:
$A O \cos 45^{\circ}=\frac{l}{2}$
$\therefore A O \times \frac{1}{\sqrt{2}}=\frac{l}{2}$
or $A O=\frac{l}{\sqrt{2}}$
$I=I_D+I_B+I_C$
or $ I=\frac{2 m l^2}{2}+m\left(\frac{2 l}{\sqrt{2}}\right)^2$
$=\frac{2 m l^2}{2}+\frac{4 m l^2}{2}$
or $ I=\frac{6 m l^2}{2}=3 m l^2$
