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

Options

A. `v=sqrt(k/(2m))R`
B. `v=sqrt(k/m)R`
C. `L=sqrt(mkR^(2))`
D. `L=sqrt((mk)/2)R^(2)`

Answer

B, C

Explanation

`U( r) = (kr^(2))/2`
`F = -(dU)/(dr)=-kr rArr (mV^(2))/R = kR`

`rArr V = sqrt(k/m)R rArr L = mV R = sqrt(mkR^(2))`