Question

The ratio of the radii of gyration of a circular disc and a circular ring of the same masses and radii about a tangential axis parallel to the their planes is:

• A. 6 : 5
• B. 1 : 2
• C. $\sqrt{5}:\sqrt{6}$
• D. none of these

Answer 1

The correct option is C $\sqrt{5}:\sqrt{6}$

$furdiscm{K}_{\alpha }^2=\frac{5}{4}m{R}^2\Rightarrow K_{\alpha }=\frac{\sqrt{5}}{2}Rforringm{K}_r^2=\frac{3}{2}m{R}^2\Rightarrow K_r=\frac{\sqrt{3}}{\sqrt{2}}R\therefore \frac{K_{\alpha }}{K_r}=\frac{\sqrt{5}}{2}\times \frac{\sqrt{2}}{\sqrt{3}}=\frac{\sqrt{5}}{\sqrt{6}}$