Question

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 0.10 m apart on a horizontal table. What is the gravitational force and potential at the mid-point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

Answer 1

Here G = 6.67 x 10^-11 Nm² kg^-2

M = 100 kg; R = 0.1 m

Distance between two spheres, d = 1.0 m

Suppose that the distance of either sphere from the mid-point of the line joining their centre is r.

Then, r = d/2 = 0.5 m

The gravitational field at the mid-point due to two spheres will be equal and opposite.

Hence, the resultant gravitational  field at the mid-point = 0

The gravitational potential at the mid-point

= (-GM/r) x 2 = (-)6.67 x 10^-11 x 100 x 2/0.5

= -2.668 x 10^-8 J kg^-1

As the net force on the body placed at midpoint zero, so the body is in equilibrium. If the body is displaced a little towards either mass body from its equilibrium position, it will not return back to its, initial position of equilibrium. Hence, the equilibrium attained is unstable.