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.

(N/A) Let the mass and radius of each identical heavy sphere be $M$ and $R$ respectively. An object of mass $m$ is placed at the mid-point $P$ of the line joining their centres.
The force acting on the object placed at the mid-point due to each sphere is $F_{1} = F_{2} = \frac{GMm}{(5R)^{2}}$. Since the directions of these forces are opposite,the net force acting on the object is zero. This is an equilibrium state.
If we move the object towards sphere $A$ by a small distance $x$,the new forces are:
$F_{1}^{\prime} = \frac{GMm}{(5R - x)^{2}}$
$F_{2}^{\prime} = \frac{GMm}{(5R + x)^{2}}$
Since $F_{1}^{\prime} > F_{2}^{\prime}$,a resultant force $(F_{1}^{\prime} - F_{2}^{\prime})$ acts on the object towards sphere $A$. As a result,the object starts to move towards sphere $A$ instead of returning to the equilibrium position. Therefore,the equilibrium is unstable.