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Q.

A 2 kg mass moving with a velocity of $10 {ms}^{- 1}$ collides with another 6 kg mass moving in opposite direction with a velocity of $20 {ms}^{- 1}$ . During the collision, they stick together. Find their common velocity and the momentum.

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a

7.5 m/s, 50 {kgms}^{- 1}

b

7.5 m/s, 100 {kgms}^{- 1}

c

12.5 m/s, 100 {kgms}^{- 1}

d

12.5 m/s, 50 {kgms}^{- 1}

answer is A.

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Detailed Solution

v_{C} = \frac{m_{1} u_{1} + m_{2} u_{2}}{m_{1} + m_{2}}

$m_{1} = 2 kg, u_{1} = 10 m/s$

$m_{2} = 6 kg, u_{2} = - 20 m/s$

$= \frac{2 (10) + 6 (- 20)}{2 + 6}$

$∴ v_{C} = \frac{- 120 + 20}{8} = \frac{- 100}{8} = - 12.5 m/s$

$P = (m_{1} + m_{2}) v_{C}$

$= (2 + 6) 12.5$

$= 100 kg m/s$

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A 2 kg mass moving with a velocity of 10 ms−1 collides with another 6 kg mass moving in opposite direction with a velocity of 20 ms−1 . During the collision, they stick together. Find their common velocity and the momentum.