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The angular momentum of a particle performing uniform circular motion is L. If the kinetic energy of the particle is doubled and frequency is halved, then angular momentum becomes

A
L2
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B
2L
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C
L4
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D
4L
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Solution

The correct option is D 4L
Angular momentum, L=Iω...........(i)
Where, I is the moment of inertia
Kinetic energy,
K=12Iω2K=12(I×ω)ωK=12Lω
(from eqn(i))
L=2Kω.......ii)
Now, given angular frequency is halved, so, let ω=ω2
And the kinetic energy is doubled, so, K=2K
If L is the new angular momentum, then using (ii) we can write,
L=2KωL=2(2K)ω2L=42KωL=4L
So, angular momentum becomes four times its original value.

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