Derive an expression for the centre of mass of a two particle system from ab-inito.

To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses serving as weights. The position of the center of mass lies closer to the particle with the larger mass. If the masses are equal, the centre of mass is exactly between the two particles. The above concept applies universally to any two-particle system, regardless of the values of distances or mass.