Question

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 4LAngular momentum, L=Iω...........(i)Where, I is the moment of inertia Kinetic energy, K=12Iω2⟹K=12(I×ω)ω⟹K=12Lω(from eqn(i))L=2Kω.......ii)Now, given angular frequency is halved, so, let ω′=ω2And the kinetic energy is doubled, so, K′=2KIf L′ is the new angular momentum, then using (ii) we can write,L′=2K′ω′⟹L′=2(2K)ω2⟹L′=42Kω⟹L′=4LSo, angular momentum becomes four times its original value.

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