Question

state the law of conservation of momentum. prove it ​

Answer 1

Answer:

For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.

Explanation:

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Answer 2

Law of conservation of linear momentum

There is no change in law of conservation of linear momentum of the body as long as no not external force acting on them.

Let us prove the law of conservation of linear momentum with the following illustration :

PROOF :

Let two bodies A and B having the masses m1 and m2 move with the initial velocity u1 and u2 in the straight line. Let the velocity of the first body be higher that of the second body. ( u1 > u2 ). During an interval of time t second, they tend to have a collision. After the impact , both of them move along the same straight line with a velocity v1 and v2 respectively.

Force on body B due to A ,

$f_{b} = \frac{ m2(v2 - u2)}{t}$

Force on body A due to B ,

$f_{a} = \frac{m1(v1 - u1)}{t}$

By Newton's second law of motion,

Action force = Reaction force

Fa = - Fb

$\frac{m1(v1 - u1)}{t} = - \frac{m2(v2 - u2)}{t}$

$m1(v1 - u1) = - m2(v2 - u2) \\ m1v1 - m2u1 = - m2v2 + m2u2 \\ m1v1 + m2v2 = m1u1 + m2u2$

The above equation confirms in the absence of an external force , the algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before collision.

Hence the law of conservation of linear momentum is proved