Two particles of masses m₁ and m₂ in projectile motion have velocities $\vec{v_{1}}$ and $\vec{v_{2}}$ respectively at time t = 0. They collide at time t_o. Their velocities become ${\vec{v_{2}}}^{1}$ and ${\vec{v_{1}}}^{1}$ at time 2t_o while 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

(m₁+m₂)gt_o

2(m₁+m₂)gt_o

$\frac{1}{2}$ (m₁+m₂)gt_o

answer is C.

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Detailed Solution

A/c L.C.L.M
$\begin{array}{l} {mv}_{1} = mv \\ {mv}_{1} = m (u + at) \\ m_{1} v_{1}^{2} + m_{2} v_{2}^{2} = m (v_{1} + 2 {gt}_{0}) + m [v_{2} + 2 {gt}_{o}] \end{array}$

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