Finding the Center of Mass of a pendulum

[antigen123]

Homework Statement

Assuming that the combined mass of the balls is greater than the combined mass of the cords, but that the cords do have some mass, where is the center of mass for the system shown below?

Homework Equations

None

The Attempt at a Solution

I tried approaching this problem by finding the center of mass for the two balls first. I picked a point closer to the lower ball which is heavier. However I don't know how I would find the center of mass of the cord?? Is the center of mass usually closer to heavier objects. I think I need a conceptual understanding of the center of mass.

 

[BvU]

well, write down the relevant equation !

The pragmatic one is: where do you support something to get a balance ? Good for individual sticks and balls. For a rope with weight: imagine it's frozen.

 

[antigen123]

My book did not give an equation for solving this particular question. However I do like the idea of finding a balance in the object in order to find the center of mass. Thanks!

 

[BvU]

The relevant equation for the position of the center of mass is
$$\vec r_{\rm c.o.m.} = {\sum_i m_i \, \vec r_i \over \sum_i m_i }$$check it out.
For each ball you end up in the center of the thing and for each section of rope you end up halfway. Comes naturally. Adding the four vectors according to the relevant formula can never let you end up at a (why not?) or at b (why not?) and some judgment about M2 > M1 leaves only one answer.