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A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass initially at rest. After collision the first mass moves with velocity $\frac{v}{\sqrt 3}$ in a direction perpendicular to its initial direction of motion. The speed of second mass after collision is
$\frac{2}{\sqrt 3}v$
$\frac{v}{\sqrt 3}$
$v$
$\sqrt 3 \,v$
Solution
$\mathrm{m}_{1} \overrightarrow{\mathrm{u}}_{1}+\mathrm{m}_{2} \overrightarrow{\mathrm{u}}_{2}=\mathrm{m}_{1} \overrightarrow{\mathrm{v}}_{1}+\mathrm{m}_{2} \overrightarrow{\mathrm{v}}_{2}$
$m\left(v^{\hat{i}}\right)+m(0)=m\left(\frac{v}{\sqrt{3}} \hat{j}\right)+m \vec{v}_{2}$
$\Rightarrow \overrightarrow{\mathrm{v}}_{2}=\mathrm{v\hat i}-\frac{\mathrm{v}}{\sqrt{3}} \hat{\mathrm{j}}$
$\therefore\left|\overrightarrow{\mathrm{v}}_{2}\right|=\sqrt{\mathrm{v}^{2}+\left(\frac{\mathrm{v}}{\sqrt{3}}\right)^{2}}=\frac{2}{\sqrt{3}} \mathrm{v}$
