Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the mid-point of the line joining their centres be in stable equilibrium or unstable equilibrium ? Give reason for your answer.

Explanation

Let the mass of each sphere be M and radius R. A point object of mass m is placed at the mid-point of line joining the two spheres as shown in figure.

Each sphere will attract the mass m with equal force of attraction, given by
`F = (GMm)/((5R)^(2))`
So, the net force acting on mass m is zero. Now, consider moving the mass m by a small amount h towards the right. Then, the forces on it are : `(GMm)/((5R-h)^(2))` to the right and `(GMm)/((5R+h)^(2))` to the left. The first is larger than the second. Hence, the net force will also be towards the right. Hence the equilibrium is unstable.