how are center of mass and center of gravity different

Question

How are center of mass and center of gravity different? Second part of question is center of mass and center of gravity are usually the same give an example of when they are different?

Answer 1

Center of mass and center of gravity are usually the same but not in all cases. They coincide when the gravitational field across the object in question is uniform. When we are very close to the surface of the earth and look at small object, this holds true. But as we go further and further away it starts decreasing from it's standard value of 9.8 m/s^2. Now say if we have a really huge object that has one end touching the surface of the earth and the other end hundreds of mile away into space, then the gravitational field across this object will not be uniform. So it's center of gravity will be different from the center of mass.

An example would be the moon rotating in earth's gravitational field. It's big, so the earth's gravitational field across the moon is not uniform. So it's center of mass will not coincide with it's center of gravity. 

Hope this answers your question.