Center of gravity and Center of mass different?!?! I was developing a test for my students and always look for a difficult question as the only bonus question. I came across the question in the book, "When are center of gravity and center of mass different?". I thought about it before looking at the book's answer; and I thought most likely when gravity varies over the object and the book agreed. Then the students argued that it could happen if there is no gravity on the object. Since CoG is the average location of an object's weight, and the object isn't massless, wouldn't the CoM & CoG be different?