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Question

# A circular disc of radius R and thickness R6 has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is

A
I
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B
2I8
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C
I5
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D
I10
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Solution

## The correct option is A I5According to problem disc is melted and recasted into a solid sphere so their volume will be same.VDisc=Vsphere ⇒πR2Disct=43πR3Sphere⇒πR2Disc(RDisc6)=43πR3Sphere [t=RDisc6,given]⇒R3Disc=8R3Sphere ⇒RSphere=RDisc2Moment of inertia of discIDisc=12MR2Disc=I (given)∴M(RDisc)2=2IMoment of inertia of sphere ISphere=25MR2Sphere=25M(RDisc2)2=M10(RDisc)2=2I10=I5.

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