Q29 of 38 Page 62

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 reason for your answer.

Given:


Distance between centres of spheres = 10 x radius


Let the mass of the two spheres be M and their radii be R. Then, the distance between the two will be 10R. let an object of mass m be placed at the midpoint of the line joining the centres of the spheres. Then the force acting on the object due to the two spheres F1 and F2 will be,



Therefore, the forces are equal and in opposite directions and therefore the mass is in stable equilibrium.


However, if the mass were to be displaced by say a distance x from the midpoint towards the sphere 2, the forces acting on the object would be




Therefore, F2’ > F1’ and therefore the net force acting on the mass will not be zero and equal to (F2’ - F1’) towards the sphere 2 and the object would be in unstable equilibrium.


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