Two bodies of masses `M_(1)` and `M_(2)` are kept separeated by a distance d. The potential at the point where the gravitational field produced by them is zero, is :-

Options

A. `-(G)/(d)(M_(1)+M_(2)+2sqrt(M_(1)M_(2)))`
B. `-(G)/(d)(M_(1)M_(2)+2sqrt(M_(1)+M_(2)))`
C. `-(G)/(d)(M_(1)-M_(2)+2sqrt(M_(1)M_(2)))`
D. `-(G)/(d)(M_(1)M_(2)-2sqrt(M_(1)+M_(2)))`

Answer

A

Explanation

`(GM_(1))/(x^(2))=(GM_(2))/((d-x)^(2))rArr(d-x)/(x)=sqrt((M_(2))/(M_(1))`
`rArr(d)/(x)=1+sqrt(M_(2))/(M_(1))rArrx=(sqrt(M_(1)d))/(sqrt(M_(1))+sqrt(M_(2)))`
Now potential `=-(GM_(2))/(x)-(GM_(2))/(d-x)`
`=(-G)/(d)(sqrt(M_(1))+sqrt(M_(2)))^(2)`