Two bodies of masses m and M are placed at distance d apart. The gravitational potential (V) at the position where the gravitational field due to them is zero V is

Options

A. `V=-(G)/(d)(m+M)`
B. `V=-(Gm)/(d)`
C. `V=-(GM)/(d)`
D. `V=-(G)/(d)(sqrt(m)+sqrt(M))^(2)`

Answer

D

Explanation

`E_("net")=0`
`:. (Gm)/(x^(2))=(GM)/((d-x)^(2)),x` is distance from `m`
`:. (x)/(d-x)=(sqrt(m))/(sqrt(M))rArrx=(sqrt(m))/(sqrt(m)+sqrt(M)),d`
and `d-x=(sqrt(M))/(sqrt(m)+sqrt(M)).d`
Since, gravitational potential between two bodies of masses M and m respectively, is given by
`V=-(Gm)/(x)-(GM)/(d-x)`
`=-(GM(sqrt(m)+sqrt(M)))/(sqrt(m).d)-(GMsqrt(m)+sqrt(M))/(sqrt(M).d)=-(G)/(d)(sqrt(m)+sqrt(M))^(2)`.