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Question

A solid sphere of radius r and mass m is rotating about an axis passing through its COM with an angular speed ω and has rotational kinetic energy k1. If the radius of the sphere is halved and angular speed is doubled, then its rotational kinetic energy becomes k2. Which of the following options is correct ?

A
k1>k2
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B
k1<k2
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C
k1=k2
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D
k1=k2=0 J
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Solution

The correct option is C k1=k2
Given,
r1=r; m1=m, ω1=ω
r2=r2; m2=m; ω2=2ω
Rotational kinetic energy of solid sphere for 1st case:
k1=12I1ω21=12(25m1r21)ω21
k1=15mr2ω2
Rotational kinetic energy of solid sphere for 2nd case:
k2=12I2w22=12(25m2r22)w22
k2=15mr2w2
k1=k20

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