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Partially Inelastic Collision

Two small bal...

Question

Two small ball $m_{1}$ and $m_{2}$ moving in opposite direction with speed 2 m/s collides. If the collision is perfectly inelastic, mass of $m_{1}$ is 3 kg and mass of $m_{2}$ is 5 kg. Calculate the speed of the objects after the collision.

A

0.25 m/s

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B

0.5 m/s

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C

0.75 m/s

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D

1 m/s

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E

2 m/s

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Solution

The correct option is C 1 m/s
Given : $m_{1} = 3 k g$ $m_{2} = 5 k g$ $u_{1} = 2 m / s$ $u_{2} = - 2 m / s$ $e = 1$
Velocities of the objects after collision be $v_{1}$ and $v_{2}$ .
Using $v_{1} = \frac{(m_{1} - e m_{2}) u_{1} + (1 + e) m_{2} u_{2}}{m_{1} + m_{2}}$

$∴$ $v_{1} = \frac{(3 - 1 \times 5) 2 + (1 + 1) 5 (- 2)}{3 + 5} = - 3 m / s$

Also using $v_{2} = \frac{(m_{2} - e m_{1}) u_{2} + (1 + e) m_{1} u_{1}}{m_{1} + m_{2}}$

$∴$ $v_{2} = \frac{(5 - 1 \times 3) (- 2) + (1 + 1) 3 (2)}{3 + 5} = + 1 m / s$
Thus speed of the objects after collision is $3 m / s$ and and $1 m / s$ respectively.

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