Advantages of studying the collision process of the centre of mass system or frame of reference:

When the origin of the reference frame system is a rigidly fixed point to the centre of mass of a system of particles then this type of frame of reference is known as centre of mass reference frame. No external force acts on the system of particles in this reference frame. The advantages of studying collisions process in the centre of mass frame of reference are \( \cdots \)

1. When there is no external force acting on the system of particles, the velocity of the centre of mass is a constant. This indicates that the centre of mass frame of reference moves with a constant velocity with respect to the laboratory frame of reference. Therefore the centre of mass frame of reference is also a inertial frame of reference. Since the velocity of centre of mass is small as compared to the velocity of light, so various physical quantities measured in the two systems are related to each other by Galelian Transformations.
2. In order to describe the motion of a system of two particles in the laboratory frame of reference, we need six co-ordinates. Three co-ordinates are required to describe the motion of the centre of mass and another three co-ordinates are required to describe the relative motion.
   On the other hand, in order to describe the motion of a system of two particles in the centre of mass frame of reference, we only need three co-ordinates, because in centre of mass frame of reference the centre of mass of the system is itself at rest.

So the study of collision process becomes more simpler in the centre of mass frame of reference than in the laboratory frame of reference.