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 `5.98xx10^(24)` kg and `7.35xx10^(23)` kg respectively and the distance between Moon and Earth is `3.85xx10^(8)`m)

Options

A. zero
B. `3.90xx10^(7)`
C. `8xx10^(8)`
D. `3.46xx10^(8)`

Explanation

Given mass of earth `M_(e )=5.98xx10^(24)`kg
mass of moon `M_(m)=7.35xx10^(22)` kg
let x be the distance of the point from the centre of earth where gravitional intensity is zero therefore
`(GM_(e ))/(x^(2))=(GM_(m))/(3.85xx10^(8)-x)^(2)`
`(x)/(3.85xx10^(8)-x)=sqrt(M_(e))/(M_(m))=sqrt(5.98xx10^(24))/(7.35xx10^(2))=9`
`rarr x=9xx3.85xx10^(8)//10`
`=3.46xx10^(8)` m