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Question

The potential energy of a mass m at a distance r from a fixed point o is given by v(r)=kr22, where k is positive constant of appropriate dimension this particle is moving in a circular orbit of radius R about the point o. If v is the speed of the particle & L is the magnitude of its angular momentum about o? Find L.

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Solution

V=kr22
F=dVdr=kr
mv2r=kr
v=kmR
Angular momentum l=mvr=mkmR2=mkR2

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