Two small balls $A$ and $B$, each of mass $m$, are connected by a light rod of length $L$. The system is lying on a frictionless horizontal surface. A particle of mass $m$ collides with the ball $B$ horizontally with a velocity $v_o$ perpendicular to the rod and gets stuck to it. Find:
(a) the angular velocity of the system after collision.
(b) the velocities of $A$ and $B$ immediately after collision.
(c) the velocity of the center of the rod when the rod rotates through $90^\circ$ degree after the collision.
As the particle collides with $B$, the rod should rotate about its new center of mass that will be at a distance $L/3$ from $B$. The net torque of this system should be zero and therefore the angular momentum about the axis of rotation will be conserved. Therefore I got $\omega$ using this.
For the second part, the answer given is, $v_A=0\,,v_B=v_o/2$.
How is this possible unless the rod rotates about $A$?
Also, how do I find the third part?
Any help suggesting how this system moves will be appreciated.