Where will two objects of different masses meet in space?

[Dumbledore211]

Homework Statement

Two objects of mass m=3kg and M=7kg are held at a distance of 10 meter in space and then released. They move towards each other due to mutual gravitation attraction. Determine the location of their meeting of the object mass m

Homework Equations

r= mr1+ Mr2/m+M

The Attempt at a Solution

The objects will meet at their center of their mass. What I am finding difficult to understand is the method of finding out r1 and r2 with respect to m from the given information

 

[Simon Bridge]

You have two variables r1 and r2 ... so you need two equations.
The other one is r=r1+r2

 

[Dumbledore211]

We really don't know the value of r which means there are actually three variables. I have tried to solve it by using your method but 2 equations won't suffice in this case. We need one more equation

 

[Chestermiller]

We really don't know the value of r which means there are actually three variables. I have tried to solve it by using your method but 2 equations won't suffice in this case. We need one more equation

You can find the center of mass using the equation:

$$x_c=\frac{\sum{mx}}{\sum{m}}$$

Take as x = 0 as the initial location of mass m.

 

[Dumbledore211]

You mean I should take r1=0 @Chestermiller

 

[Chestermiller]

You mean I should take r1=0 @Chestermiller

Yeah, although it doesn't really matter. Take the origin anywhere you want. The answer will come out the same (in terms of the distances from each of the two masses).