Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 0.1

1.	Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 0.10 m apart on a horizontal table. What is the gravitational force and potential at the mid-point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?
Answer» Here G = 6.67 x 10^-11 Nm² kg^-2 M = 100 kg; R = 0.1 m Distance between two spheres, d = 1.0 m Suppose that the distance of either sphere from the mid-point of the line joining their centre is r. Then, r = d/2 = 0.5 m The gravitational field at the mid-point due to two spheres will be equal and opposite. Hence, the resultant gravitational field at the mid-point = 0 The gravitational potential at the mid-point = (-GM/r) x 2 = (-)6.67 x 10^-11 x 100 x 2/0.5 = -2.668 x 10^-8 J kg^-1 As the net force on the body placed at midpoint zero, so the body is in equilibrium. If the body is displaced a little towards either mass body from its equilibrium position, it will not return back to its, initial position of equilibrium. Hence, the equilibrium attained is unstable.

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 0.10 m apart on a horizontal table. What is the gravitational force and potential at the mid-point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

Answer»

Here G = 6.67 x 10^-11 Nm² kg^-2

M = 100 kg; R = 0.1 m

Distance between two spheres, d = 1.0 m

Suppose that the distance of either sphere from the mid-point of the line joining their centre is r.

Then, r = d/2 = 0.5 m

The gravitational field at the mid-point due to two spheres will be equal and opposite.

Hence, the resultant gravitational field at the mid-point = 0

The gravitational potential at the mid-point

= (-GM/r) x 2 = (-)6.67 x 10^-11 x 100 x 2/0.5

= -2.668 x 10^-8 J kg^-1

As the net force on the body placed at midpoint zero, so the body is in equilibrium. If the body is displaced a little towards either mass body from its equilibrium position, it will not return back to its, initial position of equilibrium. Hence, the equilibrium attained is unstable.

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