Momentum In the figure shown the system is at rest initially. Two persons ' $A$ ' and ' $B$ ' of masses $40 kg$ each move with speeds $v_{1}$ and $v_{2}$ respectively towards each other on a plank lying on a smooth horizontal surface as shown in figure. Plank travels a distance of $20 m$ towards right direction in $5 \sec$ . (Here $v_{1}$ and $v_{2}$ are given with respect to the plank). Then the possible condition( $s$ ) can be

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$v_{1} = 0 m / s, v_{2} = 10 m / s$

$v_{1} = 5 m / s, v_{2} = 15 m / s$

$v_{1} = 2 m / s, v_{2} = 12 m / s$

$v_{1} = 10 m / s, v_{2} = 20 m / s$

answer is A, B, C, D.

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Detailed Solution

Vel. of plank $= + 4 m / s$

vel. of centre of mass, $V_{CM} = 0 = \frac{40 (v_{1} + 4) - 40 (v_{2} - 4) + 20 (4)}{40 + 40 + 20} \Rightarrow v_{2} - v_{1} = 10 m / s$

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