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JEE Main 2005 (AIEEE) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2005 (AIEEE)

Q193JEE Main 2005 · AIEEEMedium

Moment of Inertia & Radius of Gyration

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about a line perpendicular to the plane of the disc through the center is

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Answer: (c)

Every mass element of the semicircular disc lies at the same distances from the centre as in a full disc.
So the mass is spread over $r$ the same way: $I = \frac{1}{2}Mr^2$ with $M$ the semicircle's mass.
So the answer is (c) $\frac{1}{2}Mr^2$ .

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