Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the midpoint of the line joining their centres be in stable equilibrium or unstable equilibrium? Give a reason for your answer.
m1=m2=Mr=10R Let mass m is placed at the mid point P of line joining the centres of A and B sphere ∣F2∣=∣F1∣=(5R)2GMm ∣F1∣=∣F2∣=25R2GMm As the direction of force F1 and F2 are opposite (equal and opposite forces acting on m at P ) the net force F1+F2=0,(F1=−F2). m will be in equilibrium. If now m in displace by x slightly from P to A then PA=(5R−x) and PB=(5R+x) F1=(5R−x)2GMm and F2=(5R+x)2GMm ∴F2<F1 Hence the resultant force acting on P is towards A, resulting in an unstable equilibrium.
