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

Options

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

Answer

D

Explanation

If p is the point of zero intensity, then `x = (sqrt(M))/(sqrt(M) + sqrt(M)) d and d - x = (sqrt(m))/(sqrt(M) + sqrt(m)) d`
Now potential at point `p , V = V_(1) + V_(2) = (- GM)/(x) - (GM)/(d - x)`
Substituting the value of x and - x we get `V = - (G)/(d) sqrt((M)/( m)) (sqrt(m) + sqrt(m))^(2)`