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Perfectly Elastic Collision

Two balls hav...

Question

Two balls having masses $m_{1} = 5 kg$ and $m_{2} = 10 kg$ moving with velocities $u_{1} = 10 m/s$ and $u_{2} = 5 m/s$ collide elastically. Find the change in momentum of the ball having mass $m_{1}$ due to collision

110 kgm/s

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90 kgm/s

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- 100 kgm/s

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50 kgm/s

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Solution

The correct option is C $- 100 kgm/s$
Let final velocity of ball having mass $m_{1}$ is $v_{1}$ and final velocity of ball having mass $m_{2}$ is $v_{2}$ .

Given, $m_{1} = 5 kg, m_{2} = 10 kg$
$u_{1} = 10 kg, u_{2} = - 5 m/s$
As we know,
$u_{1} - u_{2} = v_{2} - v_{1}$
$15 = v_{2} - v_{1}$
$\begin{matrix} v_{2} = 15 + v_{1} \\ (1) \end{matrix}$
By using conservation of momentum
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
$(5 \times 10) + (5 \times (- 10)) = (5 \times v_{1}) + (10 \times v_{2})$
$0 = (5 \times v_{1}) + (10 \times v_{2})$
By using eq (1) in above equation we get,
$- (5 \times v_{1}) = (10 \times (15 + v_{1}))$
$- 30 = 3 v_{1}$
$v_{1} = - 10 m/s$
We know change in maomentum $Δ p = m Δ v = m (v_{f} - v_{i}) = m_{1} (v_{1} - u_{1}) = 5 (- 10 - 10) kgm/s = - 100 kgm/s$

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Two balls having masses m1=5 kg and m2=10 kg moving with velocities u1=10 m/s and u2=5 m/s collide elastically. Find the change in momentum of the ball having mass m1 due to collision

Two balls having masses $m_{1} = 5 kg$ and $m_{2} = 10 kg$ moving with velocities $u_{1} = 10 m/s$ and $u_{2} = 5 m/s$ collide elastically. Find the change in momentum of the ball having mass $m_{1}$ due to collision