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Two particles of masses m₁and m₂ in projectile motion have velocities ${\vec{v}}_{1} and {\vec{v}}_{2}$ respectively at time t = 0. They collide at time t₀. Their velocities become ${\vec{v}}_{1}^{1} and {\vec{v}}_{2}^{1}$ at time 2t₀while still moving in air. The value of $|(m_{1} {\vec{v}}_{1}^{1} + m_{2} {\vec{v}}_{2}^{1}) - (m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2})|$ is

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zero

$(m_{1} + m_{2}) {gt}_{0}$

$2 (m_{1} + m_{2}) {gt}_{0}$

$\frac{1}{2} (m_{1} + m_{2}) {gt}_{0}$

answer is C.

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Detailed Solution

$ΔP = F \times t = (m_{1} + m_{2}) g 2 t_{0}$

collision due to internal forces do not change the momentum of the system.

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