Question

# Two discs of moment of inertia I1 and I2 having angular speed ω1 and ω2 are rotating along collinear axis passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same axis the rotational KE of system will be

A
I1ω1+I2ω22(I1+I2)
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B
(I1+I2)(ω1+ω2)22
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C
(I1ω1+I2ω2)22(I1+I2)
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D
None of these
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Solution

## The correct option is C (I1ω1+I2ω2)22(I1+I2)By the law of conservation of angular momentum, I1ω1+I2ω2=(I1+I2)ω Angular velocity of system , ω=I1ω1+I2ω2I1+I2 Rotational kinetic energy =12(I1+I2)ω2=12(I1+I2)(I1ω1+I2ω2I1+I2)2 =(I1ω+I2ω2)22(I1+I2)

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