Write an expression for the position vector of the centre of mass of n-particle system. Also write the equations of motion which govern the motion of the centre of mass.

The position vector of a center of mass in an n-particle system can be determined by a weighted average of the positions of the particles, and their masses play roles as weights. This average is influenced by the total mass in the system. According to Newton’s second law, the motion of the center of mass is given by the fact that the total external force acting on the system is equal to the mass of the system multiplied by the acceleration of the center of mass. The acceleration of the center of mass is also determined by the net external forces acting on each individual particle so that it can behave like a single point mass.