Question

show that the total linear momentum of a system of particles is conserved in any collision?

Answer 1

Dear Student,

For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.
For the isolated system external for must be zero so
$$\begin{gathered} F=0 \\ weknowthat \\ F=\frac{dP}{dt}=0 \\ dP=0 \\ {P}_i=P_f \end{gathered}$$