Particle A of mass m₁ moving with velocity $\left( {\sqrt3\widehat i + \widehat j} \right)m{s^{ - 1}}$ collides with another particle B of mass m₂ which is at rest initially. Let $\overrightarrow {{V_1}}$ and $\overrightarrow {{V_2}}$ be the velocities of particles A and B after collision respectively. If m₁ = 2m₂ and after
collision $\overrightarrow {{V_1}} =$$\left( {\widehat i + \sqrt 3 \widehat j} \right)$ , the angle between $\overrightarrow {{V_1}}$ and $\overrightarrow {{V_2}}$ is :

Given m₁ = 2m₂ <br>So let, m₂ = m and m₁ = 2m <br><br>From momentum conservation <br><br>${\overrightarrow p _i}$ = ${\overrightarrow p _f}$ <br><br>$\Rightarrow$ (2m)$\left( {\sqrt 3 \widehat i + \widehat j} \right)$ + 0 = 2m$\left( {\widehat i + \sqrt 3 \widehat j} \right)$ + m${\overrightarrow V _2}$ <br><br>$\Rightarrow$ ${\overrightarrow V _2}$ = 2$\left( {\sqrt 3 \widehat i + \widehat j} \right)$ - 2$\left( {\widehat i + \sqrt 3 \widehat j} \right)$ <br><br>$\Rightarrow$ ${\overrightarrow V _2}$ = $$\left( {2\sqrt 3 - 2} \right)\widehat i - \widehat j\left( {2\sqrt 3 - 2} \right)$$ <br><br>= $2\left( {\sqrt 3 - 1} \right)\left( {\widehat i - \widehat j} \right)$ <br><br>Also given after collision $$\overrightarrow {{V_1}} = \left( {\widehat i + \sqrt3\widehat j} \right)m{s^{ - 1}}$$ <br><br>For angle between ${\overrightarrow V _1}$ &amp; ${\overrightarrow V _2}$, <br><br>cos $\theta$ = $${{{{\overrightarrow V }_1}.{{\overrightarrow V }_2}} \over {\left| {{{\overrightarrow V }_1}} \right|\left| {{{\overrightarrow V }_2}} \right|}}$$ <br><br>= $${{2\left( {\sqrt 3 - 1} \right) \times 1 - 2\left( {\sqrt 3 - 1} \right) \times \sqrt 3 } \over {2 \times 2\sqrt 2 \left( {\sqrt 3 - 1} \right)}}$$ <br><br>= $${{2\left( {\sqrt 3 - 1} \right)\left( {1 - \sqrt 3 } \right)} \over {2 \times 2\sqrt 2 \left( {\sqrt 3 - 1} \right)}}$$ <br><br>= ${{\left( {1 - \sqrt 3 } \right)} \over {2\sqrt 2 }}$ <br><br>$\Rightarrow$ $\theta$ = 105^o