Question

Calculate the ratio of radii of gyration of circular ring and a disc of the same radius with respect to the axis passing through their centres and perpendicular to their planes.

Answer 1

we have formulae,

$I_1=M{R}^2$

$k_1=R$

$I_2=\frac{1}{2}M{R}^2$

$k_2=\sqrt{\frac{1}{2}{R}^2}=\frac{R}{\sqrt{2}}$

$\therefore k_1:k_2=\sqrt{2}:1$