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Question

From a semi-circular disc of mass M and radius R2. A semi-circular disc of radius R1 is removed as shown in the figure. If the mass of original uncut disc is M, find the momentum of inertia of residual disc about an axis passing through centre O and perpendicular to the plane of the disc.
1029964_2d952b61a7f646aa921e709002bdcd7c.png

A
M2R22(R42R41)
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B
MR22(R42R41)
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C
MR22(R424R41)
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D
M2R22(R42R414)
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Solution

The correct option is A M2R22(R42R41)
momentofinertiaoftheoriginalsemicirculardiscthroughcentreandperpendiculartotheplaneofdisc=MR222planarmassdensity=2MπR22SothemassofsemicircularofradiusR1=MR12R22momentofinertiaofthesemicirculardiscofradiusR2=MR142R22momentofinertiaoftheremainingportion=MR222MR142R22=M2R22(R24R14)

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