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Question

The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire and passing through its centre is:

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

The correct option is A Mr2
consider small element of mass dm on the semicircular wire.
moment of inertial about a point at distance r is given by:
dI=dmr2
to find total moment of inertia, integrate both sides
dI=r2dm
dm=M, total mass of body.
I=Mr2.
so The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire and passing through its centre is Mr2

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