Question 18 of 130

Particle $A$ of mass ${m}_{1}$ moving with velocity $\left(\sqrt{3}\hat{i}+\hat{j}\right){ms}^{-1}$ collides with another particle $B$ of mass ${m}_{2}$ which is at rest initially. Let ${\vec{v}}_{1}$ and ${\vec{v}}_{2}$ be the velocities of particles $A$ and $B$ after collision respectively. If ${m}_{1}=2{m}_{2}$ and after collision ${\vec{v}}_{1}-\left(\hat{i}+\sqrt{3}\hat{j}\right){ms}^{-1}$, the angle between ${\vec{v}}_{1}$ and ${\vec{v}}_{2}$ is :

A${15}^{^{\circ}}$B${60}^{^{\circ}}$C$-{45}^{^{\circ}}$D${105}^{^{\circ}}$

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Answer: (D) ${105}^{^{\circ}}$

${m}_{1}{\vec{u}}_{1}+{m}_{2}{\vec{u}}_{2}={m}_{1}{\vec{v}}_{1}+{m}_{2}{\vec{v}}_{2}$
$2{m}_{2}(\sqrt{3}\hat{i}+\hat{j})+{m}_{2}\times 0=2{m}_{2}(\hat{i}+\sqrt{3}\hat{j})+{m}_{2}\times {\vec{v}}_{2}$
$2\sqrt{3}\hat{i}+2\hat{j}=2\hat{i}+2\sqrt{3}\hat{j}+{\vec{v}}_{2}$
${\vec{v}}_{2}=(\sqrt{3}-1)\hat{i}-(\sqrt{3}-1)\hat{j}$
${\vec{v}}_{1}=\hat{i}+\sqrt{3}\hat{j}$
Angle between ${\vec{v}}_{1}$ and ${\vec{v}}_{2}$ is ${105}^{^{\circ}}$