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A thin uniform circular disc of mass M a...

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 `omega` . Another disc of same dimensions but of mass `(1)/(4)` M is placed gently on the first disc co-axially. The angular velocity of the system is

A

`(5)/(4) omega`

B

`(2)/(3) omega`

C

`(4)/(5) omega`

D

`(3)/(2) omega`

Text Solution

Verified by Experts

The correct Answer is:
C
`I_(1)omega_(1)=I_(2)omega_(2)`
implies `(1)/(2)MR^(2)omega=[(1)/(2)MR^(2)+(1)/(2)((M)/(4))R^(2)]omega_(2)`
implies `omega_(2)=((1)/(2)MR^(2)omega)/((1)/(2)[MR^(2)+(MR^(2))/(4)])`
implies `omega_(2)=(4)/(5)omega`
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