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 midpoint 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

Mass of each sphere = 100 kg 

Radius of each sphere = 0.1 m

At the midpoint M, the gravitational pull by each sphere is exactly the same since they are identical spheres. 

So, The gravitational force is zero.

The potential at M =  \(_-\frac {GM}{(0.5)}\) - \(\frac {GM}{(0.5)}\)

= – 4GM

– 4 × 6.67 × 10^-11 × 100

= – 2.668 × 10^-8 J/kg

So, the potential at ‘M’ is – 2.67 × 10^-8 J/kg

At object at M will be in equilibrium. Since mt force on it is zero. The equilibrium is unstable as a slight ctange in position of the mass, the net foce becomes non zero and it will move.