A 90° arc is removed from a thin circular ring of mass M and radius R. If the moment of inertia of the remainder about the central perpendicular axis is KMR², find K.
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Question

A 90° arc is removed from a thin circular ring of mass M and radius R. If the moment of inertia of the remainder about the central perpendicular axis is KMR², find K.

G1 Physics · Accepted Answer

Step 1: The removed arc is one-quarter of the ring, so remaining mass is 3M/4. Step 2: Every element still lies at distance R from the central axis. Step 3: Thus I=(3M/4)R² and K=3/4. Final answer: A — 3/4.