Prove the law of conservation of linear momentum

Asked by admin @ 31/08/2021 in Physics viewed by 345 People

State and prove law of conservation of linear momentum.

Answered by admin @ 31/08/2021

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
$\bold{F_{ext}=0}\:\text{then},{\boxed{\boxed{\bold{P_i=P_f}}}}$

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

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