Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

Options

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

Answer

D

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) Rightarrow 1/x^2=9/((r-x)^2)`
`Rightarrow sqrt((r-x)^2)=sqrt(9x^2) Rightarrowr-x=3x`
`Rightarrow x=r/4`
Gravitational potential at this point is given by `-((4Gm)/r+(G9mxx4)/(3r)) [r-x=(3r)/4]`
`Rightarrow -((4Gm+G9m)/rRightarrow-((16Gm)/r)`