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 centers of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?
Solution
We have,
Mass of the sphere, M1=M2 = 100kg
Radius of the sphere, r = 0.10 m
Distance between the spheres, AB = R = 1m
Gravitational field due to mass M1, at P
Similarly, gravitational field due to mass M2 at P is,
Mass of the sphere, M1=M2 = 100kg
Radius of the sphere, r = 0.10 m
Distance between the spheres, AB = R = 1m
Gravitational field due to mass M1, at P
Similarly, gravitational field due to mass M2 at P is,
The gravitational field due to two masses are equal and opposite, therefore net gravitational field at P is zero.
The gravitational potential at P is,
The net gravitational field at P is zero, therefore the object placed at P will be in equilibrium.
The equilibrium is an unstable equilibrium.
