Question 22 of 130

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 ${45}^{o}$ with respect to the original direction. The speed of each of the moving particle will be

A$\sqrt{2}\text{v}$B$\dfrac{\text{v}}{\sqrt{2}}$C$2\sqrt{2}\text{v}$D$\dfrac{\text{v}}{\left(2\sqrt{2}\right)}$

Show answer and solution▾

Answer: (C) $2\sqrt{2}\text{v}$

As $2m$ splits into equal parts, ${v}_{1}={v}_{2}$ and $\theta =4{5}^{0}$
From conservation of linear momentum,
$m\left(2v\right)+2m\left(v\right)=2\left[m{v}_{1}\cos ⁡4{5}^{o}\right]$
$\Rightarrow {v}_{1}={v}_{2}=2\sqrt{2}\text{v}$