$A$ spherical ball $A$ of mass $4 \ kg$, moving along a straight line, strikes another spherical ball $B$ of mass $1 \ kg$ at rest. After the collision, $A$ and $B$ move with velocities $v_1 \ ms^{-1}$ and $v_2 \ ms^{-1}$ respectively, making angles of $30^{\circ}$ and $60^{\circ}$ with respect to the original direction of motion of $A$. The ratio $\frac{v_1}{v_2}$ will be

• A
  $\frac{\sqrt{3}}{4}$
• B
  $\frac{4}{\sqrt{3}}$
• C
  $\frac{1}{\sqrt{3}}$
• D
  $\sqrt{3}$