Q 11-06-010NEETNEET 2023Top questionMedium
The ratio of radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :
Answer: (A) $3:5$
$I = Mk^2$.
Solid sphere: $\dfrac{2}{5}MR^2 = Mk_1^2$, so $k_1^2 = \dfrac{2}{5}R^2$.
Hollow sphere: $\dfrac{2}{3}MR^2 = Mk_2^2$, so $k_2^2 = \dfrac{2}{3}R^2$.
$$\frac{k_1^2}{k_2^2} = \frac{2/5}{2/3} = \frac{3}{5} \;\Rightarrow\; \frac{k_1}{k_2} = \sqrt{\frac{3}{5}}$$
Strictly, the ratio of the radii of gyration is $\sqrt{3} : \sqrt{5}$, which is not among the options. Option (1), $3 : 5$, is the ratio of their squares, $k_1^2 : k_2^2$, and is the intended answer.
Solution by Sreeraj P, M.Sc Physics