Question

The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis perpendicular to plane of disc or ring is

• A. 1 : 2
• B. $ \sqrt{5}\,:\,\sqrt{6} $
• C. 2 : 3
• D. $ \frac{\sqrt{3}}{2} $

Answer 1

Answer: (D)

Radius of gyration $K=\sqrt{\frac{I}{m}}$
(where $I$ is moment of inertia)
$K_{d i s c}=\sqrt{\frac{\frac{1}{2} m R^{2}+m R^{2}}{m}}=\sqrt{\frac{3}{2}} R$
$K_{\text {ring }}=\sqrt{\frac{m R^{2}+m R^{2}}{m}}=\sqrt{2} R$
$\therefore \frac{K_{\text {disc }}}{K_{\text {ring }}}=\frac{\sqrt{\frac{3}{2}}}{\sqrt{2}}=\frac{\sqrt{3}}{2}$