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A $4 k g$ mass moving with a velocity of $20 m / s$ collides with another $5 k g$ mass moving in opposite direction with a velocity of $40 m s^{- 1} .$ During the collision, they stick together. Find their common velocity and the momentum.

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$- 13.3 m / s, 120 k g m s^{- 1}$

$12.5 m / s, 50 k g m s^{- 1}$

$7.5 m / s, 100 k g m s^{- 1}$

$7.5 m / s, 50 k g m s^{- 1}$

answer is A.

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Detailed Solution

$v = \frac{m_{1} u_{1} - m_{2} u_{2}}{M_{1} + M_{2}}$

$v = \frac{4 \times 20 - 5 \times 40}{9}$

$= \frac{80 - 200}{9} = \frac{- 120}{9}$

$= - 13 . 3 m / s$

Momentum $= (M_{1} + M_{2}) v$

$= (4 + 5) 13.3 = 120 k g m s^{- 1}$

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