Two bodies of masses m and 4m are placed at a distance r. Calculate the gravitational potential at a point on the joining them where the gravitational field is zero.

Explanation

G.F due to m = `(Gm)/(x^2)`
G.F due to `4m = (G.4m)/((r-x)^(2))`
Gravitational field is zero at a point.
`(Gm)/(x^2) = (G.4m)/((r-x)^(2)) implies 1/(x^2) = 4/((r-x)^(2)) implies 1/x = 2/(r -x)`
`:. R - x = 2x implies 3x = r implies x = r/3`
The gravitational potential
`=(-Gm)/(r//3) - (G.4m)/(2r//3) = (-3 Gm)/r - (6 Gm)/r`
`V(r) = (-9 Gm)/(r)`.