Q. Four particles each of mass $m$ are placed at the corners of a square of side length $\ell .$ The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is
Solution:
Moment of inertia of system about point
$P=4 m\left[\frac{1}{\sqrt{2}}\right]^{2}=2 m \ell^{2}$ and $ 4 m k^{2}=2 m \ell^{2} $
$\therefore \,\, k =\frac{\ell}{\sqrt{2}}$
