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Question

One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

A
MR28
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B
MR22
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C
MR24
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D
MR2
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Solution

The correct option is B MR22
For complete disc with mass 4M, moment of inertia about given axis =(4M)R22=2MR2

Hence, by symmetry for the given quater of disc, moment of inertia about the axis passing through the center of the original disc.
I=2MR24=MR22
I=MR22

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