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

Let gravitational field be zero at a point lying at distance x from M then
`impliesx=((sqrt(M))/(sqrt(M)+sqrt(M)))d`
`implies (d-)=((sqrt(m))/(sqrt(M)+sqrt(m)))d`
`impliesV_(p)=-(Gm)/(d-x)-(GM)/x`