Two bodies of masses `100 kg` and `10,000 kg` are at a distance `1 m` apart. At which point on the line joining them will the resultant gravitational field intensity is zero? What is the gravitational potential at that point ?
`G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.

Explanation

Let `x` be the distance of the point `P` from `100 kg` body where the resultant gravitational intensity is zero.
`:.` Gravitational intensity at `P` due to body of mass `100 kg` is equal and opposite to that due to body of mass `10,000 kg`. Hence,
`(G xx 100)/(x^(2)) = (G xx 10,000)/((1 - x)^(2))` or `100 x^(2) = (1 - x)^(2)`
or `10 x = 1 - x` or `11 x = 1` or `x = 1//11 m`
Gravitational potential at `P`
`= - (Gm_(1))/(r_(1)) + (-(Gm_(2))/(r_(2))) = - G[(m_(1))/(r_(1)) + (m_(2))/(r_(2))]`
`= - 6.67 xx 10^(-11) [(100)/(1//11) + (10,000)/(10//11)]`
`~~ - 8 xx 10^(-7) J//kg`