A smooth disc of mass `M` and radius `(L)/(sqrt(3))` is placed at rest horizontally on a smooth horizontal surface. A massless pin is fixed at point `P` at a distance `L//2` from centre `O` of the disc as shown in the figure. Now a thin uniform rod of mass `M` and length `L` is placed horizontally on the surface of the disc parallel to the line `OP` such that its mid point and centre `O` of the disc just coincide as shown in figure. Now rod has given angular velocity `omega_(0)=24 rad//sec` in counter clockwies direction as shown. As a result, the end of the rod strikes the pin `P` and stricks to it rigidly. Calculate the angular velocity of disc just after collision.

Explanation

Apply conservation of angular momentum about `O'` (below `O` lying on ground)
`(ML^(2))/(12)omega_(0)=((ML^(2))/(6)+(ML^(2))/(12))omega`