Find the point at which the gravitational force acting on any mass is zero due to the earth and the moon system. (such a point is called neutral point). The mass of the moon and the distance between the earth and the moon is 3,85,000 km.

Find the point at which the gravitational force acting on any mass is

1.	Find the point at which the gravitational force acting on any mass is zero due to the earth and the moon system. (such a point is called neutral point). The mass of the moon and the distance between the earth and the moon is 3,85,000 km.
Answer» Solution : Let `m_(1)` and `m_(2)` be the masses of the EARTH and the moon separated by a distance d. Consider an object of mass m at a point P, which is at a distance X from `m_(1)`. The force due to mass `m_(1)` on the mass m is `F_(1) = (GM m_(1))/(X^(2))` TOWARDS `m_(1)` and The force due to mass `m_(2)` on the mass m is `F_(2) = (Gm m_(2))/((d-x)^(2))` towards `m_(2)` If the RESULTANT force on the mass .m. is to be zero, `F_(1)` must be equal to `F_(2)` in magnitude and they are oppositely DIRECTE `(Gm m_(1))/(x^(2)) = (Gm m_(2))/((d-x)^(2)) rarr x = 38,500 km` from moon here `m_(1) = M` mass of the moon, `m_(2) = 81M`, mass of the earth