What is the distance of the particle from mass A?

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    Gravitation
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Homework Help Overview

The problem involves two bodies, A and B, with different masses and a small particle placed between them. The objective is to determine the distance of the particle from mass A when the net gravitational force acting on it is zero.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the setup of the gravitational force equations and question the representation of distances and forces. There is an exploration of simplifying the equations and clarifying the use of the condition that the net gravitational force is zero.

Discussion Status

The discussion is ongoing, with participants providing guidance on simplifying equations and questioning assumptions about the mass of the particle. There is no explicit consensus, but various interpretations and approaches are being explored.

Contextual Notes

Some participants note the assumption that the particle has negligible mass, while others question the relevance of this assumption to the gravitational acceleration experienced by the particle.

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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
Fx+(-Fd-x)=Gm1m2/x2-Gm1m2/(d-x)2
after simplifying
Gm1m2d2-2dxGm1m2/dx2+x4-2dx3[/B]
 
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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.
 
"the net gravitational force on the particle is zero"

Where did you use this fact? Where is 0 in your equation?
 
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
 
dean barry said:
assume the particle is of negligable mass
Why? It does not matter what its mass is, the acceleration would be the same.
dean barry said:
call the distance from A = 1,
Mr.maniac called it x, which seems even better.
 

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