Final answer:
The motion of the center of mass of a system, where an external force acts on one particle, can be described by Newton's Second Law applied to the system as a whole, using the equation F = Macm.
Step-by-step explanation:
The question regards the center of mass and its motion when an external force acts on one of several particles of a system. According to Newton's Second Law for an entire system, the acceleration of the center of mass (acm) of a system is directly proportional to the net external force (F) applied to the system and inversely proportional to the total mass (M) of the system. The relevant equation is F = Macm, where F is the external force, M is the total mass of the system, and acm is the linear acceleration of the center of mass. In the case described, despite the fact that only one particle is subject to an external force, the motion of the system's center of mass will still be influenced by this force because the center of mass responds to the external forces as if the entire mass of the system were concentrated at that point.