Question

A body of mass $m$ moves with speed $2v$ and a body of mass $2m$ moves with speed $v$ on a smooth horizontal surface, both along positive $x$ axis. After some time, they collide and stick together. What is the speed of the system after they stick together?

• A. $\frac{2v}{3}$
• B. $\frac{v}{3}$
• C. $\frac{4v}{3}$
• D. $\frac{5v}{3}$

Answer 1

The correct option is C $\frac{4v}{3}$

Since both bodies are moving along $+vex-$ axis, the initial momentum of the system is,
$\overrightarrow{P_i}=m\left(2v\right)\hat{i}+\left(2m\right)v\hat{i}$
$\overrightarrow{P_i}=4mv\hat{i}$

After collision and sticking together, let the combined mass move with velocity $v^{\prime }$ along $+vex-$axis

Since ${\overrightarrow{F}}_{\text{ext}}=0$, we can apply conservation of linear momentum on system of $m\&2m$
$\overrightarrow{P_i}=\overrightarrow{P_f}$
$4mv\hat{i}=\left(3m\right)v^{\prime }\hat{i}$
$\therefore v^{\prime }=\frac{4}{3}v$

Hence, $v^{\prime }$ is the speed of system after collision.