A circular ring has mass M and diameter r. Its moment of inertia about a tangential axis lying in the plane of the ring is:
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Question

A circular ring has mass M and diameter r. Its moment of inertia about a tangential axis lying in the plane of the ring is:

G1 Physics · Accepted Answer

The radius of the ring is R = r/2. Moment of inertia of a thin ring about a diameter in its plane is I(diameter) = MR²/2. The required tangent axis is parallel to this diameter and at distance R from the centre. By the parallel-axis theorem, I(tangent) = I(diameter) + MR² = MR²/2 + MR² = 3MR²/2. Substitute R=r/2: I(tangent) = (3M/2)(r²/4) = 3Mr²/8. Correct option: A.