Question

Law of Conservation of Linear Momentum and prove it.

Answer 1

Law of conservation of linear momentum states that totalmomentum of the system is always conserved if no external force acts on an object or system of objects.

Answer 2

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

[Note :- here doesn't include sign of velocity , but when you will solve question include direction of velocity as you know velocity is vector quantity