Two masses $m_{1}$ and $m_{2}$ collide with each other. Before the collision, the velocities are $u_{1}$ and $u_{2}$ respectively. After the collision, the velocities are $v_{1}$ and $v_{2}$ respectively. The total final momentum after collision is given by:

m_{1} v_{1} + m_{2} v_{1}

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m_{1} u_{2} + m_{2} u_{1}

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m_{1} u_{1} + m_{2} u_{2}

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m_{1} u_{1} + m_{2} v_{2}

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Solution

The correct option is C $m_{1} u_{1} + m_{2} u_{2}$
The initial momentum of body of mass $m_{1}$ is $m_{1} u_{1}$
The initial momentum of body of mass $m_{2}$ is $m_{2} u_{2}$
$∴$ Total initial momentum before collision = $m_{1} u_{1} + m_{2} u_{2}$
According to the law of conservation of momentum, the total momentum of a system is always conserved, i.e. the initial momentum is equal to the final momentum.
So we can say the total final momentum = the total initial momentum
$m_{1} v_{1} + m_{2} v_{2} =$ $m_{1} u_{1} + m_{2} u_{2}$

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