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Question

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 centre is

A
12Mr2
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B
Mr2
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C
25Mr2
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D
14Mr2
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Solution

The correct option is A 12Mr2
If M is the mass of the semi-circular disc, then the mass of the complete disc will be 2M.
Moment of inertia of complete disc about the given axis
=12(2M)r2=Mr2

The moment of inertia of the semi-circular disc is half of the Moment of inertia of the circular disc due to symmetry.
Moment of inertia of semi-circular disc =12Mr2
So, (D) is the right choice.


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