Question

how to prove newton's second law of a centre of mass system with two bodies?

Answer 1

The acceleration of center of mass of two object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the two object.
Consider two mass connected through a spring.
\[a_{cm}= F_{net} / M_{total}\]

Answer 2

thanks