Two particles of masses `m_1 and m_2` in projectile motion have velocities `vecv_1 and vecv_2` respectively at time `t=0.` They collide at time `t_0.` Their velocities become `vecv_1' and vecv_2'` at time `2t_0` while still moving in air. The value of `|(m_1vecv_1' + m_2vecv_2') - (m_1vecv_1 + m_2vecv_2)|` is

Options

A. zero
B. `(m_1+m_2)gt_0`
C. `1/2(m_1+m_2)gt_0`
D. `2(m_1+m_2)gt_0`

Answer

D

Explanation

(d) If we consider the two particle as a system then the
external force acting on the system is te gravitational
pull `(m_1+m_2)g.`
`F_(ext)=(Deltap)/(Deltat)`
`:. Deltap=F_(ext)Delta=(m_1vecv_1'+m_2vecv_2')-(m_1vecv_1-m_2vecv_2)`
`(m_1+m_2)gxx2t_0`