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

Explanation

Refer to Fig. when an object of mass `m` is placed at `P`, the mid point of `AB`, then each sphere will attract
this object with a force `F = (GM m)/((5R)^(2))`. Due to it, the
resultant force on object at `P` is zero and the object at `O` is in equilibrium. If the object is displaced a small distance `x` from `P` towards sphere `B`, then the force on object due to sphere`A, F_(1) = (GM m)/((5R + x)^(2))` acting towards sphere `A`. The force on object due to sphere `B`,
`F_(2) = (GM m)/((5R - x)^(2))` acting towards sphere `B`. As `F_(2) gt F_(1)`, so a net force will be acting on object towards sphere `B` and object will move towards `B`.
Therefore, the object will be in unstable equilbrium.