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A uniform circular ring has mass M and radius R. If a 90° arc of the ring is cut away, the moment of inertia of the remaining portion about an axis through the centre of the ring and perpendicular to its plane becomes kMR². What is the value of k?

1. 3/4
2. 7/8
3. 1/4
4. 1/8

Correct answer: 3/4

Solution

When a 90° arc is removed from the uniform circular ring, the remaining portion consists of three-quarters of the original mass and retains the same radius. The moment of inertia of the full ring is MR², and removing the arc reduces the moment of inertia proportionally, resulting in a new moment of inertia of (3/4)MR².

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