Question

Define law of conservation of linear momentum???
Also give the derivation...

Answer 1

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

Answer 2

Newton's third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum. ... B=m_{2}(v_{2}-u_{2}) (change in momentum of particle B)