Question

Two particles of masses $m_{1}$ and $m_{2}$ in projectile motion have velocities $v _{1}$ and $v _{2}$ respectively at time $t=0$. They collide at time $t_{0}$. Their velocities become $v _{1}^{\prime}$ and $v _{2}^{\prime}$ at time $2 t_{0}$ while still moving in air. The value of $\left|\left(m_{1} v _{1}^{\prime}+m_{2} v _{2}^{\prime}\right)-\left(m_{1} v _{1}+m_{2} v _{2}\right)\right|$ is

• A. zero
• B. $\left(m_{1}+m_{2}\right) g \,t_{0}$
• C. $2\left(m_{1}+m_{2}\right) g t_{0}$
• D. $\frac{1}{2}\left(m_{1}+m_{2}\right) g t_{0}$

Answer 1

Answer: (C)

$\left|\left(m_{1} v _{1}^{\prime}+m_{2} v _{2}^{\prime}\right)-\left(m_{1} v _{1}+m_{2} v _{2}\right)\right|$
$=\mid$ change in momentum of the two particles $\mid$
$=\mid$ External force on the system $\mid \times$ time interval
$=\left(m_{1}+m_{2}\right) g\left(2 t_{0}\right)=2\left(m_{1}+m_{2}\right) g t_{0}$