Distinguish between the center of mass and the center of gravity.

(N/A) The $Center \text{ of } Mass$ is a point where the entire mass of the system is assumed to be concentrated for the purpose of describing its translational motion. It depends only on the distribution of mass within the system.
The $Center \text{ of } Gravity$ is a point where the total gravitational force (weight) of the system is assumed to act. It depends on the gravitational field in which the system is placed.
Key difference: If the gravitational field is uniform,the $Center \text{ of } Mass$ and $Center \text{ of } Gravity$ coincide. If the gravitational field is non-uniform,they may differ.