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

Answer

D

Explanation

Equilibrium position of the neutral point from mass m is
`=((sqrt(m))/(sqrt(m)+sqrt(M)))d`
`V_(1)=(-Gm_(1))/(r_(1)),V_(2)=(-Gm_(2))/(r_(2))`
`V_(1)=(-Gm)/(sqrt(m)d)(sqrt(M)+sqrt(m)),V_(2)=(-GM)/(sqrt(M)d)(sqrt(M)+sqrt(m))`
`V_(1)=(-G)/(d)sqrt(m)(sqrt(M)+sqrt(m)),V_(2)=(-G)/(d)sqrt(M)(sqrt(M)+sqrt(m))`
`V=(-G)/(d)(sqrt(M)+sqrt(m))^(2)`