Two heavy spheres of mass 100 kg 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 spheres ? Is an object placed at that point in equilibrium ? Is so, is the equilibrium stable or unstable.

Two heavy spheres of mass 100 kg radius 0.10 m are placed 1.0 m apart

1.	Two heavy spheres of mass 100 kg 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 spheres ? Is an object placed at that point in equilibrium ? Is so, is the equilibrium stable or unstable.
Answer» Solution :Gravitational FIELD at the mid-point of the LINE joining the centres of the two SPHERES `= (GM)/((r//2)^(2)) (-hat(r)) + (GM)/((r//2)^(2)) hat(r) = 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 md-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 equilibirum. Hence, the body is in unstable equilibirum.