If the initial velocity of $m_{1}$ is $u m s^{- 1}$ and initial velocity of $m_{2}$ is $2 u m s^{- 1}$ . After collision $m_{2}$ stops, then what is the final velocity of $m_{1}$ after collision? If $m_{1}$ = $m k g$ and $m_{2}$ = $2 m k g$ .

10 u m s^{- 1}

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2 u m s^{- 1}

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5 u m s^{- 1}

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0 m s^{- 1}

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Solution

The correct option is C $5 u m s^{- 1}$
Given:
Mass of $m_{1}$ = $m k g$
Mass of $m_{2}$ = $2 m k g$
Initial velocity ( $u_{1}$ ) of $m_{1}$ = $u m s^{- 1}$ ;
Initial velocity ( $u_{2}$ ) of $m_{2}$ = $2 u m s^{- 1}$
Final velocity ( $v_{2}$ ) of $m_{2}$ = $0 m s^{- 1}$

Need to find:
Final velocity of $m_{1}$ = $v_{1} m s^{- 1}$

Initial momentum of the system:
$\Rightarrow$ $m_{1} u_{1} + m_{2} u_{2}$
$\Rightarrow$ $m u + 4 m u = 5 m u$
Final momentum of the system:
$\Rightarrow$ $m_{1} v_{1} + m_{2} v_{2}$
$\Rightarrow$ $m_{1} v_{1} + m_{2} (0)$
$\Rightarrow$ $m v_{1}$

So according to conservation of momentum;
Final momentum = Initial momenum
$\Rightarrow$ $m v_{1}$ = $5 m u$
$\Rightarrow$ $v_{1}$ = $5 u m s^{- 1}$

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