Center of gravity in a non uniform gravitational field

[luisgml_2000]

Hi:

I have a very big concern about my mechanics homework because a problem says: "Find a formula that gives the position of the center of gravity and make sure that in the limiting case of a uniform gravitational field your formula predicts that both center of gravity and center of mass coincide"

 

[jdavel]

luisgml,

Since you don't say what your "very big concern" is, I'll just guess: you don't understant what they're asking for.

Take a simple object - two point masses, 1kg and 2kg connected by a massless, rigid rod 1m long. Where is the center of mass?

Now suppose the gravitational field at the location of the 1kg object is twice as strong as it is at the location of the 2kg object (assume the direction of the field is the same at both locations). What seems like a reasonable definition for the "center of gravity", and where will it be?