A ball of mass 4 kg moving with a velocity of 12 m/s impinges directly on another ball of mass 8 kg moving with velocity of 4 m/s in the same direction. Find their velocities after impact (if $e$ = 0.5)

2 m/s, 4 m/s

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4 m/s, 8 m/s

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4 m/s, 6 m/s

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4 m/s, 12 m/s

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Solution

The correct option is B
4 m/s, 8 m/s

$u_{1}$ = 12 m/s $m_{1}$ = 4kg; $u_{2}$ = 4 m/s $m_{2}$ = 8 kg

Let $v_{1}$ & $v_{2}$ be the velocities after impact

Conservation of momentum: $m_{1} v_{1} + m_{2} v_{2}$ = $m_{1} u_{1} + m_{2} u_{2}$

$\Rightarrow$ $4 v_{1} + 8 v_{2}$ = 80 ............(i)

$v_{1} - v_{2} = - e (u_{1} - u_{2})$ [ $∵$ coefficient of restitution = $\frac{v e l o c i t y o f s e p a r a t i o n}{v e l o c i t y o f a p p r o a c h}$ ]

$v_{1} - v_{2} = - 0.5 (12 - 4)$ = -4 ..............(ii)

Solving (i) & (ii), we get: $v_{1}$ = 4 m/s $v_{2}$ = 8 m/s

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A ball of mass 4 kg moving with a velocity of 12 m/s impinges directly on another ball of mass 8 kg moving with velocity of 4 m/s in the same direction. Find their velocities after impact (if e = 0.5)

A ball of mass 4 kg moving with a velocity of 12 m/s impinges directly on another ball of mass 8 kg moving with velocity of 4 m/s in the same direction. Find their velocities after impact (if $e$ = 0.5)