In the above problem the angular velocity of the system after the particle sticks to it will be?

In the above problem the velocity of the centre of mass after 1 sec will be :

A uniform disc of mass m and radius R rotates about a fixed vertical axis passing through its centre with angular velocity omega . A particle of same angular velocity mass m and moving horizontally with velocity 2omegaR towards centre of the disc collides and sticks to its rim. The angular velocity of the disc after the particle sticks to it is

In the above question, the angular velocity will:

In the above question, the angular velocity will: