Answer
The answer is given below.
Work Step by Step
We can define the center of mass so its motion obeys Newton's law. $\vec F=ma_{cm}$ with F the net external force on the system & M is the total mass. When gravity is the only external force, then the center of mass has the trajectory of a particle. But if the net external force is zero, then the center of mass acceleration $\vec a_{cm}$ is also zero, and the center of mass moves with constant velocity. But the system at rest, the center of mass remains at rest despite any motions of its internal parts
