The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

Question

Aicharya · Accepted Answer

$I_{	ext {Ring }}=M R^{2}+M h^{2}=M R^{2}+M R^{2}=2 M R^{2}$ $I_{	ext {Disc }}=\frac{1}{2} M R^{2}+M h^{2}=\frac{1}{2} M R^{2}+M R^{2}=\frac{3}{2} M R^{2}$ $	herefore k_{	ext {ring }}=\sqrt{2} R$ $\quad k_{	ext {disc }}=\sqrt{\frac{3}{2}} R$ $	herefore \frac{k_{	ext {ring }}}{k_{	ext {disc }}}=\frac{\sqrt{2}}{\sqrt{3}}=\frac{2}{\sqrt{3}}$

The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a…

Solution