The moment of inertia of a solid sphere of mass $M$ and radius $R$ about its own axis is $I_{\text{solid}} = \frac{2}{5}MR^2$. Its radius of gyration $K_{\text{solid}} = \sqrt{\frac{I_{\text{solid}}}{M}} = \sqrt{\frac{2}{5}}R$.

The moment of inertia of a thin hollow sphere (spherical shell) of mass $M$ and radius $R$ about its axis is $I_{\text{hollow}} = \frac{2}{3}MR^2$. Its radius of gyration $K_{\text{hollow}} = \sqrt{\frac{I_{\text{hollow}}}{M}} = \sqrt{\frac{2}{3}}R$.

The ratio of their radii of gyration is: $\frac{K_{\text{solid}}}{K_{\text{hollow}}} = \frac{\sqrt{\frac{2}{5}}R}{\sqrt{\frac{2}{3}}R} = \sqrt{\frac{2}{5} \times \frac{3}{2}} = \sqrt{\frac{3}{5}}$. Thus, the ratio is $\sqrt{3}:\sqrt{5}$.