Question

Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in the figure. They collide completely inelastically and move as a single particle $C$. The angle $\theta$ that the path of $C$ makes with the $X-axis$ is given by :

• A. $\tan \theta =\frac{\sqrt{3}+\sqrt{2}}{1-\sqrt{2}}$
• B. $\tan \theta =\frac{\sqrt{3}-\sqrt{2}}{1-\sqrt{2}}$
• C. $\tan \theta =\frac{1-\sqrt{2}}{\sqrt{2}(1+\sqrt{3})}$
• D. $\tan \theta =\frac{1-\sqrt{3}}{1+\sqrt{2}}$

Answer 1

Answer: (A)

$2m{v}^{\prime }sin\theta =\frac{mv}{\sqrt{2}}+\frac{mv\sqrt{3}}{2}$
$3m{v}^{\prime }cos\theta =\frac{mv}{2}-\frac{mv}{\sqrt{2}}$
$sin\theta =\frac{\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}}{\frac{1}{2}-\frac{1}{\sqrt{2}}}$
$=\frac{\sqrt{2}+\sqrt{3}}{1-\sqrt{2}}$