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

let two spheres are located at A and B and P is the midpoint of separation between them.
Given, mass of sphere, M1 = M2 = M = 100kg
radius of sphere, r1 = r2 = 0.1m
and distance between them, AB = 1m
here, P is the midpoint of AB.
so, AP = PB = AB/2 = 0.5m

now, gravitational field at p due to A = GM1/(AP)²
gravitational field at p due to B, = GM2/(PB)²
Here, net gravitational field = GM/(AP)² (along PA) + GM/(PB)² ( along PB) = 0 [ magnitude of gravitational fields is same. But directed in just opposite direction ]

Hence, net gravitational field at midpoint , P = 0 so, gravitational force = 0 at midpoint, P

gravitational potential at P = -GM/AP - GM/AP
= -GM/0.5 - GM/0.5

= -2GM/0.5

= -4GM

= -4 × 6.67 × 10^-11 × 100

= -2.67 × 10^-8 J/kg

yes , object placed at that point in equilibrium. and that is unstable equilibrium.

Answer 2

Explanation:

Explain why the maximum height of mountain on earth is approximately 10 km?

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?