Two heavy sphere each of mass `100 kg` and radius `0.10 m` are placed `1.0 m` apart on a horizontal table. What is the gravitational field and potential at the mid point of the line joining the centres of the sphere? Is an object placed at that point in equilibrium? If so, is the equilbrium stable or unstable.

Explanation

Gravitational field at the mid-point of the line joining the centres of two spheres
`= (GM)/((r//2)^(2)) (-hatr) + (GM)/((r//2)^(2)) hatr = 0`
Gravitational potential at the mid point of the line joining the centres of the two spheres is
`V = - (GM)/(r//2) + ((-GM)/(r//2)) = (-4GM)/(r) = (-4 xx 6.67 xx 10^(-11) xx 100)/(1.0) = - 2.7 xx 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 little 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.