$A$ uniform rod of length $8 a$ and mass $6 m$ lies on a smooth horizontal surface. Two point masses $m$ and $2 m$ moving in the same plane with speed $2 v$ and $v$ respectively strike the rod perpendicularly at distances $a$ and $2 a$ from the mid point of the rod in the opposite directions and stick to the rod. The angular velocity of the system immediately after the collision is:

• A
  $\frac{6 v}{32 a}$
• B
  $\frac{6 v}{33 a}$
• C
  $\frac{6 v}{40 a}$
• D
  $\frac{6 v}{41 a}$