State and prove the law of conservation of linear momentum .

1.	State and prove the law of conservation of linear momentum .
Answer» Solution :Law statesthat " There is no changein the LINEARMOMENTUM of a system of bodies as long as no net external force acts on them " Proof: Lettwo bodies A and B havingmasses `m_1` and `m_2` MOVE with initial velocity `u_1 and u_2` in a straight LINE . LET the velocity of the firstbody be higherthan that of the second body . i.e., `u_1 gt u_2` . Duringan interval of time t second , they tendto havea collision . Afterthe impact, both of them move along the same straightline with a velocity `v_1 and v_2` respectively . Forceon body B due to A , `F_B=m_1(v_1-u_1)//t` Forceon body A due to B , `F_A=m_2(v_2-u_2)//t` By Newton's III lawof motion , Action force = Reaction force `F_A=-F_B` `(m_2(v_2-u_2))/(cancel(t))= (-m_1(v_2-u_2))/(cancel(t))` `m_1v_1=m_2v_2=m_1u_1+m_2u_2`-------------(A) The aboveequation confirmsin the absenceof an external force , the algebraic sum of the momenutm after collison is numerically equal to the algebraic sum of the MOMENTUM before collision . Hence the law ofconservation of linearmomentum is proved.

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