Two particles of masses `m_1 and m_2` in projectile motion have velocities `u_1 and u_2` respectively at time `t=0`. They collide at time `t_0`. Their velocities become `v_1 and v_2` at time `2t_0` while still moving in air. The value of `[(m_1v_1+ m_2v_2)-(m_1 u_1 - m_2u_2)]` is

Options

A. zero
B. `(m_1 + m_2) g t_0`
C. `2(m_1 + m_2) g t_0`
D. `1/2 (m_1 + m_2) g t_0`

Answer

C

Explanation

From `t_1 = 0` to `2t_0` the external force acting on the combined system is `m_1g + m_2g`
`therefore` Total change in momentum of the system `implies F xx t = (m_1 + m_2) g xx 2t_0`