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Question

A concentric hole of radius R/2 is cut from a thin circular plate of mass M and radius R. The moment of inertia of the remaining plate about its axis will be

A
1324MR2
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B
1124MR2
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C
1332MR2
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D
1532MR2
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Solution

The correct option is C 1332MR2
MomentofinertiaofthecutdiscportionaboutO=I1MomentofinertiaofremainingportionaboutO=I2M.IofthefulldiscaboutO=II=I1+I2Massofoutdisc=MR2(R2)2=M4I1aboutO=12(M4)(R2)2=MR232I1aboutO=MR232+M4(R4)=MR232+MR216=3MR232I2=II1=MR223MR232=13MR232
Hence,
option (C) is correct answer.

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