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

Explanation

Gravitational field at the mid - point of the line joining the centre of the 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 = (-4xx6.67 xx10^(-11) xx100)/(0.1) = -2.7 xx10^(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.