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Question

A circular disc of radius r and mass m is rotating about an axis passing through its COM perpendicular to its plane with an angular speed ω. If the radius of the disc is halved and the angular speed is doubled, which of the following options is correct?

A
K.E1=K.E22
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B
K.E1=2K.E2
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C
K.E1=K.E2
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D
K.E1=K.E24
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Solution

The correct option is C K.E1=K.E2
Given,
r1=r,m1=m,w1=w
r2=r2;m2=m;w2=2w
Rotational kinetic energy for 1st case: (K.E1)=12I1w21
=12(m1r212)w21
Rotational kinetic energy for 2nd case: (K.E2)=12I2w22
=12(m2r222)w22

K.E1K.E2=r21r22×w21w22
K.E1K.E2=(2rr)2(w2w)2=1
K.E1=K.E2

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