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 :-
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)))`
Text Solution
Verified by Experts
The correct Answer is:
A
`(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)`
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