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The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is
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$\sqrt{5}: \sqrt{6}$
$\begin{aligned} & \mathrm{I}_{\text {disk }}=\frac{5}{4} \mathrm{MR}^2=\mathrm{MK}_{\text {disk }}^2 \\ & \mathrm{I}_{\text {ring }}=\frac{3}{2} \mathrm{MR}^2=\mathrm{MK}_{\text {ring }}^2 \\ & =\frac{\mathrm{K}_{\text {disk }}}{\mathrm{K}_{\text {ring }}}=\sqrt{\frac{\overline{5}}{6}}\end{aligned}$
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