The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is

Moment of inertia of rod of mass M and length / about its axis passing through one of its ends and perpendicular to it is

    I = $\frac{1}{3}{\mathrm{MI}}^2$

As I = ${\mathrm{Mk}}^2$ where k is the radius of the gyration

$\therefore {\mathrm{Mk}}^2 = \frac{1}{3}{\mathrm{Ml}}^2 \mathrm{or} \mathrm{k} = \frac{\mathrm{l}}{\sqrt{3}}$