Radius of spheres is given as
Distance between two spheres is given as
Mass of each sphere is given as
We can infer from the figure that ‘A’ is the mid-point. Since each sphere will exert the gravitational force in the opposite direction, so the gravitational force at this point will be zero.
The gravitational potential at the midpoint can be calculated as:
As a result, the gravitational potential and force at the mid-point of the line connecting the centres of the two spheres is
The net force on an object, placed at the mid-point is zero. But, even if their is a little displacement towards any of the two bodies, it will not return to its equilibrium position. Therefore, the body is in an unstable equilibrium.