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A particle performing uniform circular m...

A particle performing uniform circular motion gas angular momentum `L`. If its angular frequency is double and its kinetic energy halved, then the new angular momentum is :

A

2L

B

4L

C

`L//2`

D

`L//4`

Text Solution

Verified by Experts

The correct Answer is:
D
`L=mv_(1)r_(1) KE_(2) =1/2KE_(1) rArr V_(2)^(2) = V_(1)^(2)/2 rArr V_(2) = V_(1)/sqrt(2) rArr 2pi f_(2)r_(2) = (2pi f_(1)r_(1))/sqrt(2)`
`rArr 2f_(1)r_(2) = (f_(1)r_(1))/sqrt(2) rArr r_(2)=r_(1)/(2sqrt(2)), L_(2) = mv_(2)r_(2) =(mv_(1))/sqrt(2) r_(1)/(2sqrt(2)) = L/4`
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