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A thin and circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. If the another disc of same dimensions but of mass M/4 is placed gently on the first disc co-axially, then the new angular velocity of the system is:

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a

54ω

b

23ω

c

45ω

d

32ω

answer is C.

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Detailed Solution

I1ω1=I2ω212MR2ω=12MR2+12M4R2ω2ω2=45ω

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A thin and circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. If the another disc of same dimensions but of mass M/4 is placed gently on the first disc co-axially, then the new angular velocity of the system is: