Question

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.

Answer 1

Let the mass and radius of each identical heavy sphere be M and A respectively. An object of mass m be placed at the mid-point P of the line joining their centres

Force acting on the object placed at the mid-point,

`F_1 = F_2 = (GMm)/(5R)^2`

The direction of forces is opposite, therefore net force acting on the object is zero. To check the stability of the equilibrium, we displace the object through a small distance x towards sphere A.

Now, the force acting towards sphere `A, F_1^' = (GMm)/(5R - x)^2`

Force acting towards sphere `B, F_2^' = (GMn)/(5R + x)^2`

As `F_1^' > F_2^'`, therefore a resultant force `(F_1^' - F_2^')` acts on the object towards sphere A, therefore, the object starts to move towards sphere A and hence equilibrium is unstable.