Question

Two spheres $A$ and $B$ of masses $m_1$ and $m_2$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $v$ along $x$-axis. After collision, $B$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction.

• A. Same as that of $B$
• B. $\theta ={\tan }^{-1}\left(\frac{1}{2}\right)\text{to the y-axis}$
• C. $\theta ={\tan }^{-1}\left(\frac{1}{2}\right)\text{to the x-axis}$
• D. Opposite to that $B$

Answer 1

The correct option is C $\theta ={\tan }^{-1}\left(\frac{1}{2}\right)\text{to the x-axis}$


Conservation of linear momentum,
In horizontal direction,
$m_1{v}_1\cos \theta =m_2{v}_2$

$\Rightarrow m_1{v}_1\cos \theta =m_{2}v$ ........$\left(1\right)$

In vertical direction,
$m_1{v}_1\sin \theta =m_2\frac{v}{2}$ ........$\left(2\right)$

Dividing equation$\left(2\right)$ by $\left(1\right)$, we get,
$\tan \theta =\frac{\frac{v}{2}}{v}$

$\Rightarrow \tan \theta =\frac{1}{2}$

$\Rightarrow \theta ={\tan }^1\left(\frac{1}{2}\right)$ to $x$-axis.

Hence, option $\left(A\right)$ is correct.