Match List-I with List-II regarding the radius of gyration ( k ) of various uniform symmetric bodies of radius R . List-I (Body and Axis) List-II (Radius of Gyration) A. Thin ring about its diameter I. R 2 B. Thin uniform disc about its diameter II. R 2 C. Solid sphere about its diameter III. 2 5 R D. Hollow sphere about its diameter IV. 2 3 R Choose the correct answer from the options given below:

Step-by-step solution

The radius of gyration k is given by k = I M . A. For a thin ring about its diameter, I = MR^2 2 k = R 2 . (Matches II) B. For a thin uniform disc about its diameter, I = MR^2 4 k = R 2 . (Matches I) C. For a solid sphere about its diameter, I = 2 5 MR^2 k = 2 5 R . (Matches III) D. For a hollow sphere about its diameter, I = 2 3 MR^2 k = 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