Two stationary particles of masses `M_(1)` and `M_(2)` are 'd' distance apart. A third particle lying on the line joining the particles, experiences no resultant gravitational force. 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_(2)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)/(1)-1=(sqrt(M_(2)))/(sqrt(M_(1)))impliesr=d[(sqrt(M_(1)))/(sqrt(M_(1)+sqrt(M_(2))))]`