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)
$K_{disc}=\sqrt{\frac{\frac{1}{2}m{R}^2+m{R}^2}{m}}=\sqrt{\frac{3}{2}}R$
$K_{\text{ring }}=\sqrt{\frac{m{R}^2+m{R}^2}{m}}=\sqrt{2}R$
$\therefore \frac{K_{\text{disc }}}{K_{\text{ring }}}=\frac{\sqrt{\frac{3}{2}}}{\sqrt{2}}=\frac{\sqrt{3}}{2}$