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 earth is 81 times the mass of the moon and the distance between the earth and the moon is 3,85,000km.

Explanation

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 the mass `m_1` on the mass m is `F_(1) = (G"mm"_1)/X^2` towards `m_1` and
The force due to the mass m, on the mass m is
`F_(2) = ("Gmm")/((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 directed `("Gmm"_1)/x^2= ("Gmm"_2)/((d-x)^2)implies` x = 38,500 km from moon, here `m_1` = M mass of the moon, `m_2 = 81 M` mass of the earth