question_answer 54)

                  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:

                  When an object is placed at the mid-point of die line joining the centres of two spheres, then each sphere attracts this object towards itself with equal forces. Thus, the net force acting oil the object is zero, and it is in equilibrium. Let die object is displaced from position P towards sphere B through a distance \[x\]. In this case force acting oil the object due to sphere B increases \[\left( F=\,\frac{G\,{{m}_{1}}{{m}_{2}}}{{{r}^{2}}} \right)\] and the force acting on the object due to sphere decreases.                 Therefore, the net force acting on the object will be towards the sphere B and hence the object will be in unstable equilibrium.