Question

Two particles of masses $m$ and $2m$ moving in opposite direction collides elastically with velocities $2v$ and $v$ respectively. Find their respective magnitude of velocities after the collision.

• A. $2v,v$
• B. $v,2v$
• C. $v,v$
• D. $4v,0$

Answer 1

The correct option is A $2v,v$

Let the final velocities of $m$ and $2m$ be $v_1$ and $v_2$ respectively.



By conservation of momentum in $x-$direction, we get:

$m\left(2v\right)+2m(-v)=m\left(v_1\right)+2m\left(v_2\right)$

$0=m{v}_1+2m{v}_2$

$\begin{array}{}\therefore v_1+2v_2=0& \text{(1)}\end{array}$
Also the collision is elastic,
$\Rightarrow$speed of separation = speed of approach

$\therefore v_2-v_1=2v+v$

Or, $\begin{array}{}{v}_2-v_1=3v& \text{(2)}\end{array}$
Solving the above two equations, we get

$v_1=-2v$ and $v_2=v$

Hence, mass $m$ moves with speed $2v$ along $-ve$,$x-$direction and mass $2m$ moves with speed $v$ in the $+ve$ $x-$direction.