1.

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.

Answer»

Solution :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.


Discussion

No Comment Found