In a conservative force field we can find the radial component of force from the potential energy function by using `F = -(dU)/(dr)`. Here, a positive force means repulsion and a negative force means attraction. From the given potential energy function U(r ) we can find the equilibrium position where force is zero. We can also find the ionisation energy which is the work done to move the particle from a certain position to infinity.
Let us consider a case in which a particle is bound to a certain point at a distance r from the centre of the force. The potential energy of the particle is : `U(r )=(A)/(r^(2))-(B)/(r )` where r is the distance from the centre of the force and A andB are positive constants. Answer the following questions.
If the total energy of the particle is `E=-(3B^(2))/(16A)`, and it is known that the motion is radial only then the velocity is zero at

Options

A. `(r_(0))/(3)`
B. `(2r_(0))/(3)`
C. `r_(0)`
D. `(2r_(0))/(5)`

Answer

B