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A uniform semicircular lamina has mass M and radius r. Its moment of inertia about an axis perpendicular to its plane and passing through the centre is

1. 2/5 Mr²
2. 1/4 Mr²
3. 1/2 Mr²
4. Mr²

Correct answer: 1/2 Mr²

Solution

For a full disc I = (1/2)MR^2. A semicircular lamina is half the disc with half the mass, so the ratio I/M is unchanged: I = (1/2)Mr^2 about the perpendicular axis through the centre.

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