Show that the radii of gyration of a circular ring and circular disc of the same radius about an axis passing through their centres and perpendicular to their plane are in the ratio `sqrt(2) : 1`.

Explanation

Here, moment of inertia of circular ring about the given axis is `I_(1) = MK_(1)^(2) = MR^(2)` ..(i)
and moment of inertia of circular disc about the same axis is `I_(2) = MK_(2)^(2) = (1)/(2)MR^(2)` ..(ii)
Dividing (i) by (ii), we get `(K_(1)^(2))/(K_(2)^(2))` or `(K_(1))/(K_(2)) = (sqrt(2))/(1)`