At what distance (in metre) from the centre of the Moon, the intensity of gravitational field will be zero? (Take, mass of Earth and Moon as 5.98 10²⁴ ~kg and 7.35 10²² ~kg respectively and the distance between Moon and Earth is 3.85 10^8 ~m .)

Step-by-step solution

Let X be the distance of the point from the centre of earth where gravitational intensity is zero. Therefore, GM _ e x ^2 = GM _ m (3.85 10^8- x )^2 or x 3.85 10^8- x = M _ e M _ m = 5.98 10²⁴ 7.35 10²² 9 or x 9 +x=3.85 10^8 or x =9 3.85 10^8 / 10=3.46 10^8 ~m Distance from Moon =3.85 10^8-3.46 10^8=3.9 10^7 ~m 3.85 10^7 ~m