Q. Four particles each of mass $m$ are placed at the corners of a square of side length $l$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is
A) $\frac{l}{\sqrt{2}}$
B) $\frac{l}{2}$
C) $l$
D) $\left( \sqrt{2} \right)l$
Explanation
(a) Moment of inertia of system about point $P$
$= 4m\left( \frac{l}{\sqrt{2}} \right)^{2} = 2ml^{2}$
and $4mK^{2} = 2ml^{2}$
$\therefore K = \frac{l}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.