A system consists of 2 particles of the same mass. Let one particle be at rest and another particle have an acceleration of “2a”. What would be the acceleration of the centre of mass of the system?

The center of mass of a distribution of mass in space is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration.