Two bodies of masses 4m and 9m are seperated by distance 'r' . The gravitational potential at a point on this line joining them where the gravitational field becomes zero is

Options

A. `(-25 Gm)/(r)`
B. `(-4Gm)/(r)`
C. `(-9 Gm)/(r)`
D. `(-13 Gm)/(r)`

Answer

A

Explanation

Atb the position when the gravitational field is zero. (Distance x is measured from 4 m mass)
`(G(4m))/(x) = (G(9m))/((r-x))`
`(4)/(x) =(9)/(r-x)`
4(r - x) = 9x
4r - 4x = 9x
4r = 9x + 4x
4r = 13 x
`x = (4)/(13) r`
The point p is at a distance `(4)/(13) r` from mass 4m and `(h - (4)/(13)r) =(9r)/(13) ` from mass m
` v = - (G(4m))/(((4)/(13)r)) -(G(9m))/((9r)/(13)) `
` v = - (26 Gm)/(r)`
Option (a) is nearest but none of the option is matching .