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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