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

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