The radius of gyration of a thin uniform circular disc (of radius R...

Moment of inertia of the thin uniform circular disc of mass $M$ and radius $R$ about an axis passing through its centre and lying in its plane (i.e., about its diameter) is
From (i) and (ii), we get $k^2=\frac{R^2}{4} \quad$ or $\quad k=\frac{R}{2}$