Question

State the law of conservation of linear momentum and prove it on the basis of second law of motion

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

Answer 2

acc. to law of conservation of momentum, when no external force acts on object, the momentum remain conserved.

acc. to second law of motion , the force applied on an object is equal to rate of change of energy,

$force = \frac{change \: in \: momentum}{time}$

let the momentum be p1 and p2 and no external force act on the object.

force=0

$0 = \frac{p2 - p1}{time} \\ 0 = p2 - p1 \\ p1 = p2$

hence proved