What is the distance of the particle from mass A?

[Mr.maniac]

Homework Statement

Two bodies A and B having masses m and 2m respectively kept at a distance of d apart.
A small particle is kept between A and B such that the net gravitational force on the particle
is zero due to the bodies A and B . Its distance from mass A should be ?

Homework Equations

The Attempt at a Solution

x= distance of the particle from A
F_x+(-F_d-x)=Gm₁m₂/x²-Gm₁m₂/(d-x)²
after simplifying
Gm₁m₂d²-2dxGm₁m₂/dx²+x⁴-2dx³[/B]

 

[Tallus Bryne]

Remember that object A has mass m and object B has mass 2m. Try simplifying again and be more clear with how you represent your fractions.

 

[Irene Kaminkowa]

"the net gravitational force on the particle is zero"

Where did you use this fact? Where is 0 in your equation?

 

[dean barry]

assume the particle is of negligable mass, then the equation for gravitational acceleration is : g = (G * M) / d^2
use substitution, call the distance from A = 1, then find the distance B

 

[haruspex]

assume the particle is of negligable mass

Why? It does not matter what its mass is, the acceleration would be the same.

call the distance from A = 1,

Mr.maniac called it x, which seems even better.