Question

A mass $'m'$ moves with a velocity $'v'$ 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)

$\frac{2}{\sqrt{3}}\,v$

Answer 2

In $x$-direction $mu_1 + 0 = 0+ mv_x$ $\Rightarrow mv=mv_{x}$ $\Rightarrow v_{x}=v$ In $y$-direction $0+0=m\left(\frac{v}{\sqrt{3}}\right)$ $\therefore$ Velocity of second mass after collision $v'=\sqrt{\left(\frac{v}{\sqrt{3}}\right)^{2}+v^{2}}=\sqrt{\frac{4}{3}\,v^{2}}$ $\therefore v '=\frac{2}{\sqrt{3}}\,v$