Q. Two particles of masses $m_{1}$ and $m_{2}$ in projectile motion have velocities ${\overrightarrow{v}}_{1}$ and ${\overrightarrow{v}}_{2}$ respectively at time $t = 0$. They collide at time $t_{0}$. Their velocities become ${\overrightarrow{v}'}_{1}$ and ${\overrightarrow{v}'}_{2}$ at time $2t_{0}$ while still moving in air. The value of $\left\lbrack \left( m_{1}{\overrightarrow{v}'}_{1} + m_{2}{\overrightarrow{v}'}_{2} \right) - (m_{1}{\overrightarrow{v}}_{1} - m_{2}{\overrightarrow{v}}_{2}) \right\rbrack$ is
A) Zero
B) $\left( m_{1} + m_{2} \right)gt_{0}$
C) 2$\left( m_{1} + m_{2} \right)gt_{0}$
D) $\frac{1}{2}\left( m_{1} + m_{2} \right)gt_{0}$
Explanation
(c) From $t_{1} = 0$ to $t_{2} = 2t_{0}$ the external force acting on the combined system is $m_{1}g + m_{2}g$
$\therefore$ Total change in momentum of system
$= Ft = \left( m_{1} + m_{2} \right)g2t_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.