A uniform cylinder of radius R and height H is filled with water to a height $\frac{2}{3}$H. It is set into rotation with constant angular velocity $\omega$  about its axis of rotation such that entire liquid have same  $\omega$. Choose the correct Statement(s)
 

The free surfaces touches first the brim of the cylinder and then the base of the cylinder when $\omega$ is gradually increased.

The free surface cannot touch the base without spilling water

The free surface touches the brim as well as the base at the same value of  $\omega$ 

At all non-zero angular speeds, shape of the free surface of liquid is paraboloid