1)

The potential energy of mass m at a distance r from a fixed point O is  given  by V(r)=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?


A) V=k2mR

B) V=kmR

C) L=mkR2

D) L=mk2R2

Answer:

Option B,C

Explanation:

V=Kr22

F=dVdr=Kr   [ towars centre]

                                                 [ F=dVdr ]

 2182019490_cir.JPG

kR=mv2R  [Centripetal force ]

v=kR2m=kmR

                        L=mvR=kmR2