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Show that the total momentum of system o...

Show that the total momentum of system of particles is equal to the product of total mass of system and velocity of centre of mass.

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According to equation (2) as in question 19.
`MvecV=m_(1)vec(v_(1))+m_(2)vec(v_(2))+...m_(n)vec(v_(n))" "...(1)`
According to chapter 4, `vecp=mvecvand(dvecp)/(dt)=vecF` Now, the linear momentum of system of n particle is equal to the vector sum of individual linear momentum of all particles of the system.
`therefore vecP=vec(p_(1))+vec(p_(2))+...vec(p_(n))`
`vecP=m_(1)vec(v_(1))+m_(2)vec(v_(2))+...m_(n)vec(v_(n))" "...(2) [because vecp=mvecv]`
Comparing equation (1) and (2),
`vecP=MvecV" "...(3)`
Hence, the linear momentum of system of particle is equal to the product of total mass of system and velocity of centre of mass.
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