Question

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 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

The gravitational field at the mid-point of the line joining the centers of the two spheres $=\frac{GM}{(r/2{)}^2}-\frac{GM}{(r/2{)}^2}=0N$
Gravitational potential at the midpoint of the line joining the centres of the two spheres is $V=-\frac{GM}{r/2}-\frac{GM}{r/2}=-\frac{4GM}{r}$

$V=-\frac{4\times 6.67\times {10}^{-11}\times 100}{0.1}$

$=-2.68\times {10}^{-7}J/kg$

As the effective force on the body placed at mid-point is 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 body is in an unstable equilibrium.