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Question

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

A
10I7
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B
2I3
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C
7I10
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D
5I10
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Solution

## The correct option is C 7I10Let the density of material be ρSo m=πr2ρr/6So I=mr22Mass will remain same , so m=4πr3sρ3=πr2ρr/6So rs=r/2MI of sphere Icm=2mr2s5The moment of inertia of the sphere about a tangent as axis of rotation isIt=2mr2s5+mr2s=7mr2s5=7mr220=7I10

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