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The ratio of the radii of gyration of a ...

The ratio of the radii of gyration of a circular disc to that of circular ring, each of same mass and same radius about their axes is

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Moment of inertia of disc about the axis of centre `I_("disc") = (MR^2)/(2) ` (or) `K_("disc") = (R)/(sqrt2)`
Moment of inertia of ring. `I_("ring") = MR^2 ` (or) `K_("ring") = R`
`(K_("disc"))/(K_("ring")) = (R//sqrt2)/(R) = 1/sqrt2 implies K_("disc") : K_("ring") = 1:sqrt2`
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