Two particles of masses `m_(1)` and `m_(2)` in projectile motion have velocities `vec(v)_(1)` and `vec(v)_(2)` , respectively , at time `t = 0`. They collide at time `t_(0)`. Their velocities become `vec(v')_(1)` and `vec(v')_(2)` at time ` 2 t_(0)` while still moving in air. The value of `|(m_(1) vec(v')_(1) + m_(2) vec(v')_(2)) - (m_(1) vec(v)_(1) + m_(2) vec(v)_(2))|`

Answer

C

Explanation

By applying impulse-momentum theorem
`=|(m_(1)vec(v)_(1) + m_(2)vec(v)_(2)) - (m_(1)vec(v)_(1) + m_(2)vec(v)_(2))|`
`= |(m_(1) + m_(2)) vec(g) (2L_(0))| - 2(m_(1) + m_(2)) g t_(0)`