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Question

# A solid sphere of mass M and radius R is rotating about its diameter. A hollow sphere of same mass and same external radius is also rotating with an angular speed twice that of solid sphere. The ratio of their kinetic energies of rotation (ES:EH) will be

A
3:20
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B
1:10
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C
20:3
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D
10:1
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Solution

## The correct option is A 3:20We know Moment of inertia of solid sphere IS=25MR2 Moment of inertia of hollow sphere IH=23MR2 Also, Kinetic energy of rotation E=12Iω2 For solid sphere, ES=12ISω2S For hollow sphere, EH=12IHω2H Given: ωH=2ωS ∴ESEH=12ISω2S12IHω2H =12×(25MR2)ω2S12×(23MR2)(2ωS)2 =25×32×14 ⇒ESEH=320

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