Question

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

• A. $\sqrt{2}v$
• B. $\frac{v}{\sqrt{2}}$
• C. $\frac{v}{\left(2\sqrt{2}\right)}$
• D. $2\sqrt{2}v$

Answer 1

The correct option is D $2\sqrt{2}v$

According to the question,

Final condition,

As we know that, in collision, linear momentum is conserved in both $x$ and $y$ directions separtely.
So, $(P_x{)}_{intial}=(P_x{)}_{final}$
$m\left(2v\right)+2m\left(v\right)=0+m{v}^{\prime }\text{cos}{45}^{\circ }+m{v}^{\prime }\text{cos}{45}^{\circ }$
$\Rightarrow 4mv=\frac{2m}{\sqrt{2}}{v}^{\prime }$
$\Rightarrow v^{\prime }=2\sqrt{2}v$