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A thin uniform 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. Another disc of same dimensions but of mass 14M is placed gently on the first disc co-axially. The angular velocity of the system is

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a

23ω

b

45ω

c

34ω

d

13ω

answer is B.

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Detailed Solution

∴I1=MR22 and I2=MR22+12M4R2=58MR2By conservation of angular momentum,Iω1=I2ω2⇒ω2=I1I2ω1=(1/2)MR2(5/8)MR2ω⇒ω2=45ω
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A thin uniform 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. Another disc of same dimensions but of mass 14M is placed gently on the first disc co-axially. The angular velocity of the system is