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Question

The potential energy of a particle of mass m at a distance r from a fixed point O is given by V(r)=kr2/2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If v is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true ?

A
v=k2m R
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B
v=km R
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C
L=mk R2
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D
L=mk2 R2
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Solution

The correct option is B v=km R
Given potential energy V=kr22
F=kr (towards centre) [F=dVdr]
At r=R,
kR=mv2R [Centripetal force]
where v is the speed of the particle

velocity v=kR2m=kmR
L=mvR=mkmR2

828396_903940_ans_401c588dfa8b4ac78f654619b68a2203.png

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