Prove the law of conservation of linear momentum use it to find the recoil velocity ofa gun when a bullet is fired from it

Prove the law of conservation of linear momentum use it to find the re

1.	Prove the law of conservation of linear momentum use it to find the recoil velocity ofa gun when a bullet is fired from it
Answer» Solution :(i) The forceon eachparticle ( Newton'ssecondlaw) can be written as ` vecF_(12) = ( dvecp_(1))/(dt)and vecF_(21) = ( dvecP_(2))/(dt)` (ii)Here ` vecP_(1)` is the MOMENTUMOF particle1 whichchanges due to the FORCE` vecF_(12)`exertedby particle 2. Further ` vecP_(2)`is the momentumof particle 2. Thischanges due to ` vecF_(21)`exertedby particle 1 . ` ( dvecp_(1))/(dt) = - (dvecp_(2))/( dt)` ` ( dvecP_(1))/( dt)+ ( d vecP_(2))/(dt) = 0` ` d/( dt)( vecP_(1) + vecP_(2)) = 0` (iii) It impliesthat ` vecP_(1) + vecP_(2)` = constantvector ( always) (iv) `vecP_(1) + vecP_(2) ` is the totallinearmomentumof thetwoparticles` ( vecP_(" tot"= vecP_(1) + vecP_(2))` . It is also called as total linear momentumof the SYSTEM. Here , the two particles constitutethe system. (v) Ifthere are no externalforcesactingon thesystem,then the totallinear momentumof thesystem ` (vecP_(" tot"))`is alwaysa constantvector .