A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

The correct answer is Rise from the sides.

When a cylindrical vessel containing water is rotated about its vertical central axis, the liquid experiences a centrifugal force in the rotating frame of reference. This force acts radially outwards, away from the axis of rotation.

The centrifugal force on a liquid particle of mass m at a distance r from the axis of rotation is given by:

$F=m{\omega }^{2}r$

where $\omega$ is the angular velocity of the vessel.

Because this outward force increases with the distance r from the center, liquid is pushed toward the outer walls of the container. To balance this force along with gravity, the liquid redistributes itself such that the pressure gradient is perpendicular to the effective gravity.
As a result, the water level goes down in the middle (near the axis of rotation) and rises along the sides of the cylinder, forming a parabolic profile known as a paraboloid of revolution. Thus, the surface rises from the sides.