The potential energy of a particle in a force field is:
`U = (A)/(r^(2)) - (B)/(r )`,. Where `A` and `B` are positive
constants and `r` is the distance of particle from the centre of the field. For stable equilibrium the distance of the particle is

Options

A. `(B)//(2A)`
B. `(2A)//(B)`
C. `(A)//(B)`
D. `(B)//(A)`

Answer

B

Explanation

`U=(A)/(r^2)-(B)/(r )=Ar^-2-Br^-1`
`F=-(dU)/(dr)=-[A(-2)r^-3-B(-1)r^-2]=0`
`-(2A)/(r )+(B)/(r^2)=0impliesr=(2A)/(B)`