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 AI5 According to problem disc is melted and recasted into a solid sphere so their volume will be same. VDisc=Vsphere
⇒RSphere=RDisc2 Moment of inertia of disc IDisc=12MR2Disc=I (given) ∴M(RDisc)2=2I Moment of inertia of sphere ISphere=25MR2Sphere =25M(RDisc2)2=M10(RDisc)2=2I10=I5.