state and Prove the principle of law of conservation of linear momentum

Dear Student,Law of conservation of linear momentum :- when there is no any external force applied on a system of particles then , momentum of system of particles will be conserved or you can say that if external force is zero. Then momentum of system of particles in intially = momentum of system of particles in finally. Mathematically, From Newton's second law, Fext = dP/dt If Fext = 0, ∫ dP =∫ 0.dt Means dP = 0 e.g., Pi = Pf Let two bodies A and B of masses m₁ and m₂ are moving with velocities u₁ and u₂ , after collision velocities of bodies are v₁ and v₂ respectively. Then, initial momentum of bodies ,Pi= m₁u₁ + m₂u₂ Final momentum of bodies, Pf = m₁v₁ + m₂v₂ Because external force doesn't apply here, so, linear momentum will be conserved . e.g., Pi = Pf m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ Regards