Question

THE LINEAR MOMENTUM OF SYSTEM OF Two PARTICLES RELATIVE TO CENTRE OF MASS IS ALWAYS ​

Answer 1

Answer:

The linear momentum of a system measured w.r.t the center of mass (CoM) frame is identically zero.

Mathematically, this can be shown as the following.

Linear momentum wrt CoM can be written as

p⃗ com=∑imi(ri→˙−v⃗ com)p→com=∑imi(ri→˙−v→com)

p⃗ com=∑imiri→˙−∑imiv⃗ comp→com=∑imiri→˙−∑imiv→com

p⃗ com=∑imiri→˙−Mv⃗ comp→com=∑imiri→˙−Mv→com