Question:
8.21) Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 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:
Gravitational field at the mid-point of the line joining the centres of the two spheres
= GM/(r/2)2 (alog negative r) + GM/(r/2) (along r) = 0
Gravitational potential at the midpoint f the line joining the centres of the two spheres is
V = - GM/r/2 + (-GM/r/2) = -4GM/r = -4 × 6.67 × 10-11 × 100/1.0
= -2.7 × 10-8 J/Kg
As the effective force on the body placed at mid-point is zero, so the body is in equilibrium. If the body is displaced a small towards either mass body from its equilibrium position, it will not return back to its initial position of equilibrium. Hence, the body is in unstable equilibrium.
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