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Question

A thin uniform circular disc of mass M and radius R is rotating with angular velocity Ω in a horizontal plane about an axis passing through its centre and perpendicular to its plane. If an another disc of same dimensions but M4 in mass is placed coaxially on first disc gently, then the angular velocity of the system now becomes

A
25ω
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B
14ω
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C
54ω
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D
45ω
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Solution

The correct option is B 45ω
We have τ=dLdt
since τ=0, L= constant
I1ω1=I2ω2
Here I1=12MR2
ω1=ω
I2=12MR2+12M4R2=(4+18)MR2=58MR2
ω2=I1ω1I2=82×5ω=45ω

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