Match List-I with List-II. List-I List-II (A) Uniform ring about its central axis (I) 2 5 R (B) Uniform disc about its central axis (II) 2 3 R (C) Solid sphere about its diameter (III) R (D) Hollow sphere about its diameter (IV) R 2 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 uniform ring about its central axis, I = MR^2 , so k = R . (B) For a uniform disc about its central axis, I = 1 2 MR^2 , so k = R 2 . (C) For a solid sphere about its diameter, I = 2 5 MR^2 , so k = 2 5 R . (D) For a hollow sphere about its diameter, I = 2 3 MR^2 , so k = 2 3 R . Therefore, the correct matching is (A)-(III), (B)-(IV), (C)-(I), (D)-(II). Answer: (A)-(III), (B)-(IV), (C)-(I), (D)-(II)