There is no change in the linear momentum of a system of bodies as long as no net external force acts on them.

**PRINCIPLE OF
CONSERVATION OF LINEAR MOMENTUM**

There is no change in
the linear momentum of a system of bodies as long as no net external force acts
on them.

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

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. Let the velocity of the first body be
higher than that of the second body. i.e., u_{1}>u_{2} .
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}â€“u_{2})/t

Force on body A due to
B,

F_{A} = m_{1}
(v_{1}â€“u_{1})/t

By Newtonâ€™s III law of
motion,

Action force = Reaction
force

F_{A} = â€“F_{B}

m_{1} (v_{1}-u_{1})/t = â€“m_{2}
(v_{2}-u_{2})/t

**m _{1}v_{1} + m_{2}v_{2} = m_{1}u_{1}
+ m_{2}u_{2} ------ (1.9) **

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 linear momentum is proved.

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10th Science : Chapter 1 : Laws of Motion : Principle of Conservation of Linear Momentum |

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