What is the difference between the center of mass and the center of gravity, and how do they relate to each other in terms of an object's stability and balance?

The center of mass is the point where an object's mass is evenly distributed in all directions, while the center of gravity is the point where the force of gravity acts on an object. The center of mass and center of gravity are typically at the same location for objects on Earth.

In terms of stability and balance, an object is stable when its center of mass is located directly above its base of support. If the center of mass is outside the base of support, the object may tip over. The center of gravity affects an object's stability because it determines how the object responds to external forces like gravity or a push.