Two stationary particles of masses `M_(1)` and `M_(2)` are at a distance d apart. A third particle, lying on the line joining the particles experiences no resultant gravitational forces. What is the distance of this particle from `M_(1)`.

Explanation

Let m be the mass of the third particle
Force on m towards `M_(1)` is `F_(1)=(GM_(1)m)/r^(2)`
Force on m towards `M_(2)` is `F_(2)=(GM_(2)m)/((d-r)^(2))`
Since net force on m is zero `:. F_(1)=F_(2)`
`implies (GM_(1)m)/r^(2)=(GM_(2)m)/((d-r)^(2))implies ((d-r)/r)^(2)=M_(2)/M_(1)implies d/r-1=sqrt(M_(2))/sqrt(M_(1))implies r=d [sqrt(M_(1))/(sqrt(M_(1))+sqrt(M_(2)))]`