Explain the meaning of law of conservation of linear momentum

Explanation

(i) There is no change in the linear momentum of a system of bodies as long as no net external force acts on them.
(ii) Let up prove the law of conservation of linear momentum with the following illustration:

(iii) Let two bodies A and B having masses `m_1 and m_2` move with initial velocity `u_1 and u_2` in a straight line.
(iv) Let hte velocity of the first body be higher than that of the second body. i.e., `u_1 > u_2`
(v) 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 `v_1 and v_2` respectively.
Force on body B due to A , `F_B = (m_2[v_2 - u_2])/(t)`
Force on body A due to B, `F_A = (m_1[v_1 - u_1])/(t)`
By Newton.s III law of motion,
Action force = Reaction force
`F_A = -F_B`
`(m_1[v_1 - u_1])/(t) = -(m_2[v_2 - u_2])/(t)`
`m_1v_1 - m_1u_1 = -m_2v_2 + m_2u_2`
`m_1v_1 + m_2v_2 = m_1v_1 + m_2 v_2`
The above equation confirms in the absence of an external force, hte algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before colliosion. Hence the low of conservation linear momentum is proved.