Match List-I with List-II List-I List-II (A) Moment of inertia of solid sphere of radius R about any tangent. (I) 5 3 MR 2 (B) Moment of inertia of hollow sphere of radius R about any tangent. (II) 7 5 MR 2 (C) Moment of inertia of circular ring of radius R about its diameter. (III) 1 4 MR 2 (D) Moment of inertia of circular disc of radius R about any diameter. (IV) 1 2 MR 2

Step-by-step solution

For solid sphere I 0 = I com   + M R 2 (Using parallel axis theorem) I 0 = 2 5 M R 2 + M R 2 I 0 = 7 5 M R 2 ⇒ A → I I For hollow sphere I = I com + M R 2 ⇒ I = 5 3 M R 2 ⇒ B → I For Circular ring I 1 + I 2 = I 3 ( Using perpendicular axis theorem) By symmetry MOI About 1 and 2 Axis are same i.e. I 1 = I 2 ∴     2 I 1 = I 3 = M R 2       ∵ I c o m = M R 2 I 1 = M R 2 2 ⇒   C → I V Similarly in disc 2 I 1 = M R 2 2 ∵ I com