What is the center of velocity of the system after the collision?

v

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- v

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\frac{5}{3} v

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3 v

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5 v

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Solution

The correct option is A $v$
Given : $m_{1} = 2 m$ $v_{1} = 2 v$ $m_{2} = m$ $v_{2} = - v$
Velocity of centre of mass of the system before collision $V_{c m} = \frac{m_{1} v_{1} + m_{2} v_{2}}{m_{1} + m_{2}}$
$∴$ $V_{c m} = \frac{2 m \times 2 v + m \times (- v)}{2 m + m} = v$
As net external force acting on the system is zero during the collision, thus velocity of centre of mass of the system remains the same before and after the collision.
Thus velocity of centre of mass of the system after collision $V_{c m}^{'} = V_{c m} = v$

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