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Q.

The potential energy of a particle of mass m at a distance r from a fixed point O is given by Vr=kr22.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?

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a

v=k2mR

b

v=kmR

c

L=mkR2

d

L=mk2R2

answer is B.

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Detailed Solution

V=kr22F=-dVdr=−kr At r=R,kR=mv2R(Centripetal force) v=kR2m=kmRAngular Momentum=L=mvR=mkmR2=mkR2

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The potential energy of a particle of mass m at a distance r from a fixed point O is given by Vr=kr22.where is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If 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?