# A body of mass

Question:

A body of mass $m_{1}$ moving with an unknown velocity of $v_{1} \hat{i}$, undergoes a collinear collision with a body of mass $m_{2}$ moving with a velocity $v_{2} \hat{i}$. After collision, $m_{1}$ and $m_{2}$ move with velocities of $v_{3} \hat{i}$ and $v_{4} \hat{i}$, respectively.

If $m_{2}=0.5 \mathrm{~m}_{1}$ and $v_{3}=0.5 v_{1}$, then $v_{1}$ is :

1. (1) $v_{4}-\frac{v_{2}}{2}$

2. (2) $v_{4}-v_{2}$

3. (3) $v_{4}-\frac{v_{2}}{4}$

4. (4) $v_{4}+v_{2}$

Correct Option: , 2

Solution:

$m_{1} v_{1}+m_{2} v_{2}=m_{1} v_{2}+m_{2} v_{1}$

or $m_{1} v_{1}+\left(0.5 m_{1}\right) v_{2}=m_{1} 0.5 v_{1}+\left(0.5 m_{1}\right) v_{4}$

On solving, $v_{1}=v_{4}-v_{2}$