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 x 10²⁴ kg and 7.35 x 10²² kg respectively and the distance between
moon and earth is 3.855x 108 m.) [JIPMER 2018] 

Given, $M_e=5.98\times {10}^{24} \mathrm{kg},M_m=7.35\times {10}^{22} \mathrm{kg}$  and

$r=3.855\times {10}^8 \mathrm{m}$

Let x be the distance of the point from the centre of earth, where gravitational intensity is zero. Therefore,

$\frac{G{M}_e}{x^2}=\frac{G{M}_m}{{\left(3855\times {10}^8-x\right)}^2}$

or     $\frac{x}{3.855\times {10}^8-x}=\sqrt{\frac{M_e}{M_m}}=\sqrt{\frac{598\times {10}^{24}}{7.35\times {10}^{22}}}\cong 9$

or     $\frac{x}{9}+x=3855\times {10}^8$

or    $x=9\times 3.855\times {10}^8/10=3.469\times {10}^8 \mathrm{m}$

Distance from moon  $=3.855\times {10}^8-3.469\times {10}^8$

                                   $=3.86\times {10}^7 \mathrm{m}$

                                    $\cong 3.85\times {10}^7 \mathrm{m}$