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Question

Moment of inertia of a thin semi circular disc ( mass=M & radius=R) about an axis through point O and perpendicular to plane of disc, is given by :
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A
14MR2
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B
12MR2
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C
18MR2
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D
MR2
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Solution

The correct option is B 12MR2
We know that the moment of inertia of a whole circle with mass M is I=12MR2. But in this case the mass of half of the circle is M so 2M will be the mass of the whole circle.
So the moment of inertia of the whole of the circle is 2×I=2×12MR2=MR2 and then the moment of inertia of half of the circle is half of this value i.e. I=12MR2.

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