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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» <html><body><p></p>Solution :(i) The forceon eachparticle ( Newton'ssecondlaw) can be written as <br/> ` vecF_(<a href="https://interviewquestions.tuteehub.com/tag/12-269062" style="font-weight:bold;" target="_blank" title="Click to know more about 12">12</a>) = ( dvecp_(1))/(dt)and vecF_(21) = ( dvecP_(2))/(dt)`<br/>(ii)Here ` vecP_(1)` is the <a href="https://interviewquestions.tuteehub.com/tag/momentumof-2840779" style="font-weight:bold;" target="_blank" title="Click to know more about MOMENTUMOF">MOMENTUMOF</a> particle1 whichchanges due to the <a href="https://interviewquestions.tuteehub.com/tag/force-22342" style="font-weight:bold;" target="_blank" title="Click to know more about FORCE">FORCE</a>` vecF_(12)`exertedby particle 2. Further ` vecP_(2)`is the momentumof particle 2. <br/>Thischanges due to ` vecF_(21)`exertedby particle 1 . <br/>` ( dvecp_(1))/(dt) = - (dvecp_(2))/( dt)` <br/>` ( dvecP_(1))/( dt)+ ( d vecP_(2))/(dt) = 0` <br/>` d/( dt)( vecP_(1) + vecP_(2)) = 0`<br/> (iii) It impliesthat ` vecP_(1) + vecP_(2)` = constantvector ( always) <br/> (iv) `vecP_(1) + vecP_(2) ` is the totallinearmomentumof thetwoparticles` ( vecP_(" tot"= vecP_(1) + vecP_(2))` . It is also called as total linear momentumof the <a href="https://interviewquestions.tuteehub.com/tag/system-1237255" style="font-weight:bold;" target="_blank" title="Click to know more about SYSTEM">SYSTEM</a>. Here , the two particles constitutethe system. <br/> (v) Ifthere are no externalforcesactingon thesystem,then the totallinear momentumof thesystem ` (vecP_(" tot"))`is alwaysa constantvector .</body></html>


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