Question

Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

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

Answer 1

Answer: (B)

$\sqrt{\frac{5}{6}}$

For disc
$M{K}_1^2=\frac{5}{4}M{R}^2⟹K_1=\frac{\sqrt{5}}{2}R$ (Ref. Image [i])
For Ring
$M{K}_2^2=\frac{3}{2}M{R}^2⟹K_2=\sqrt{\frac{3}{2}}R$ (Ref. Image [ii])
So $\frac{k_1}{k_2}=\frac{\sqrt{5}\times \sqrt{2}}{2\times \sqrt{3}}=\sqrt{\frac{5}{6}}$