For a disc about an axis passing through its centre and normal to its plane, $I_1 = \frac{MR^2}{2}$. The radius of gyration $k_1 = \sqrt{\frac{I_1}{M}} = \frac{R}{\sqrt{2}}$. For a disc about its diameter, $I_2 = \frac{MR^2}{4}$. The radius of gyration $k_2 = \sqrt{\frac{I_2}{M}} = \frac{R}{2}$. The ratio $k_1 : k_2 = \frac{R}{\sqrt{2}} : \frac{R}{2} = \sqrt{2} : 1$.