Rotation 5 Question 10

20. The potential energy 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=k2mR

(b) v=kmR

(c) L=mkR2

(d) L=mk2R2

(2018 Adv.)

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Answer:

Correct Answer: 20. (b,c)

Solution:

  1. V=Kr22

F=dVdr=Kr( towards centre )F=dVdr

kR=mv2R( Centripetal force )v=kR2m=kmRL=mvR=mkR2



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