Question

A mass ${}^{\prime }{m}^{\prime }$ moves with a velocity ${}^{\prime }{v}^{\prime }$ and collides inelastically with another identical mass. After collision the $1^{st}$ mass moves with velocity $\frac{v}{\sqrt{3}}$ a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision :

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

Answer 1

Answer: (C)

In $x$-direction
$m{u}_1+0=0+m{v}_x$
$\Rightarrow mv=m{v}_x$
$\Rightarrow v_x=v$
In $y$-direction
$0+0=m\left(\frac{v}{\sqrt{3}}\right)$
$\therefore$ Velocity of second mass after collision
$v^{\prime }=\sqrt{{\left(\frac{v}{\sqrt{3}}\right)}^2+v^2}=\sqrt{\frac{4}{3}{v}^2}$
$\therefore v^{\prime }=\frac{2}{\sqrt{3}}v$