Two particles of masses `m` and `9m` are separated by a distance `r`. At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is (G = Universal constant of gravitation)

Options

A. `-(4 Gm)/(r )`
B. `-(8Gm)/(r )`
C. `-(16 Gm)/(r )`
D. `(32 Gm)/(r )`

Answer

C

Explanation

According to question for the given system of particles
Let at point p gravitational field is zero so
`(Gm)/(x^(2))=(G9m)/(r-x)^(2) rarr (1)/(x^(2))=(9)/(r-x)^(2)`
`rarr sqrt(r-x)^(2)=sqrt(9x^(2)) ararrr-x=3x`
`rarr x=(r )/(4)`
Gravitational potential at this point is given by
`-(4Gm)/(r )+(G9mxx4)/(3r)[r-x=(3r)/(4)]`
`rarr -(4gm+12Gm)/(r)rarr-(165Gm)/(r )`