Match List-I with List-II regarding the radius of gyration ( k ) of...

The radius of gyration $k$ is given by $k = \sqrt{\dfrac{I}{M}}$.

A. For a thin ring about its diameter, $I = \dfrac{MR^2}{2} \implies k = \dfrac{R}{\sqrt{2}}$. (Matches II)

B. For a thin uniform disc about its diameter, $I = \dfrac{MR^2}{4} \implies k = \dfrac{R}{2}$. (Matches I)

C. For a solid sphere about its diameter, $I = \dfrac{2}{5}MR^2 \implies k = \sqrt{\dfrac{2}{5}}R$. (Matches III)

D. For a hollow sphere about its diameter, $I = \dfrac{2}{3}MR^2 \implies k = \sqrt{\dfrac{2}{3}}R$. (Matches IV)

Therefore, the correct matching is A-II, B-I, C-III, D-IV.

Answer: A-II, B-I, C-III, D-IV