### Q.21:- 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 centers of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium

stable or unstable?

**Answer:-**

Grvitational field at the mid-point of the line joining the centres of the two spheres

= G*M*/(*r*/2)^{2} (alog negative *r*) + G*M*/(*r*/2) (along *r*) = 0

Gravitational potential at the midpoint f the line joining the centres of the two spheres is

*V* = – G*M*/*r*/2 + (-G*M*/*r*/2) = -4G*M*/*r* = -4 × 6.67 × 10^{-11} × 100/1.0

= -2.7 × 10^{-8} J/Kg

As the effective force on the body placed at mid-point is zero, sso 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 inital position of equilibrium. Hence, the body is in unstable equilibrium.