Two bodies of equal masses (M) moving with equal velocities (V) in opposite direction collide. Resultant velocity of the combination:

V

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V a

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- V

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Zero

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Solution

The correct option is C Zero
Given : $m_{1} = m_{2} = M$ $v_{1} = V$ $v_{2} = - V$

Momentum of $m_{1}$ is $P_{1} = M V$
Momentum of $m_{2}$ is $P_{2} = - M V$
Their sum is $P_{R} = P_{1} + P_{2} = M V - M V = 0$ . . . . (i)

Let us consider the resultant velocity of the system as $V_{R}$
Resultant mass of the system be $M_{R} = m_{1} + m_{2} = 2 M$
The Resultant momentum of the system $P_{R} = M_{R} V_{R} = 2 M V_{R}$ . . . . (ii)

Comparing (i) and (ii),
$2 M V_{R} = 0$
$\Rightarrow V_{R} = 0$

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