Question

A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass at rest. After collision, the first mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. The speed of the $2^{\text {nd }}$ mass after collision is

• A. $\frac{2 v}{\sqrt{3}}$
• B. $\frac{v}{\sqrt{3}}$
• C. $v$
• D. $\sqrt{3} v$

Answer 1

Answer: (A)

In $x$ -direction $m v+0=0+m v_{1} \cos \theta \dots$ (i)
where $v_{1}$ is the velocity of $2^{\text {nd }}$ mass. In $y$ -direction
$0=\frac{m v}{\sqrt{3}}-m v_{1} \sin \theta$
or $ m v_{1} \sin \theta=\frac{m v}{\sqrt{3}} \dots$(ii)
Squaring and adding eqns. (i) and (ii), we get
$v_{1}^{2}=v^{2}+\frac{v^{2}}{3}=\frac{4 v^{2}}{3}$
$ \therefore v_{1}=\frac{2 v}{\sqrt{3}}$