A uniform rod of length 8a and mass 6m lies on a smooth horizontal surface. Two points masses m and 2m moving in the same plane with speed 2v and v respectively strikes the rod perpendicularly at distances a and 2a 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 :

Question

\[\begin {array} {1 1} (a)\;\frac{6v}{32 a} & \quad (b)\;\frac{6v}{33a} \\ (c)\;\frac{6v}{40a} & \quad (d)\;\frac{6v}{41 a} \end {array}\]