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A horizontal disc rotates freely about a...

A horizontal disc rotates freely about a vertical axis through its centre. A ring, having the same mass and radius as the disc, is now gently placed on the disc. After some time, the two rotate with a common angular velocity, then

A

Some friction exists between the disc and the ring

B

the angular momentum of the “disc plus ring” is conserved

C

The final common angular velocity is 2/3rd of the initial angular velocity of the disc

D

(2/3)rd of the initial kinetic energy changes to heat

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`K_(1) =1/2(1/2mr^(2)) omega_(1)^(2) = 1/4 mr^(2)omega_(1)^(2)`
`rArr K_(2) =1/2 {1/2 mr^(2) + mr^(2)} omega_(2)^(2)= 1/2 m^(2)omega_(1)^(2) = K_(1)/3 rArr` Energy lost `=K_(1) -K_(2) = 2K_(1)//3`
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