A particle of mass $m$ is moving with speed $2\text{v}$ and collides with a mass $2m$ moving with speed $\text{v}$ in the same direction. After the collision, the first mass is stopped completely while the second one splits into two particles each of mass $m,$ which move at an angle ${45}^{\mathrm{o}}$ with respect to the original direction. The speed of each of the moving particle will be

• A

  $\sqrt{2}\text{v}$
• B

  $\frac{\text{v}}{\sqrt{2}}$
• Correct answer
  C

  $2\sqrt{2}\text{v}$
• D

  $\frac{\text{v}}{\left(2\sqrt{2}\right)}$

Solution

As $2\mathrm{m}$ splits into equal parts, ${\mathrm{v}}_1={\mathrm{v}}_2$ and $\mathrm{\theta }=45^0$
From conservation of linear momentum,
$\mathrm{m}\left(2\mathrm{v}\right)+2\mathrm{m}\left(\mathrm{v}\right)=2\left[\mathrm{m}{\mathrm{v}}_1\cos 45^{\mathrm{o}}\right]$
$\Rightarrow {\mathrm{v}}_1={\mathrm{v}}_2=2\sqrt{2}\text{v}$

Hence, the correct answer is option: 'C'.