A ball of mass $10 k g$ is moving with a velocity of $10 m / s$ . It strikes another ball of mass $5 k g$ , which is moving in the same direction with a velocity of $4 m / s$ . If the collision is elastic their velocities after the collision will be respectively.

8 m / s, 10 m / s

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6 m / s, 10 m / s

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6 m / s, 12 m / s

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8 m / s, 12 m / s

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Solution

The correct option is C $6 m / s, 12 m / s$
Mass of first ball is $m_{1} = 10 k g$ and its velocity before collision $u_{1} = 10 m / s$
Mass of second ball is $m_{2} = 5 k g$ and its velocity before collision $u_{2} = 4 m / s$
Velocity of first ball after collision $v_{1} = \frac{(m_{1} - e m_{2}) u_{1} + (1 + e) m_{2} u_{2}}{m_{1} + m_{2}}$
where $e = 1$ (elastic collision)
$∴$ $v_{1} = \frac{(10 - 1 \times 5) (10) + (1 + 1) (5) (4)}{10 + 5} = 6 m / s$
Velocity of second ball after collision $v_{2} = \frac{(m_{2} - e m_{1}) u_{2} + (1 + e) m_{1} u_{1}}{m_{1} + m_{2}}$
$∴$ $v_{2} = \frac{(5 - 1 \times 10) (4) + (1 + 1) (10) (10)}{10 + 5} = 12 m / s$

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