Final answer:
Centripetal force in a rotating cylindrical vessel causes the liquid to rise at the sides; the difference in height of the liquid at the center and at the sides can be calculated based on the radius and rotation frequency and is about 4 cm in this case.
Step-by-step explanation:
When a cylindrical vessel containing a liquid is rotated about its axis, the centripetal force causes the liquid to rise along the sides while lowering at the center, creating a parabolic surface. The difference in the height of the liquid depends on the rotation frequency and the radius of the cylinder. In this case, with a radius of 5 cm and a rotation frequency of 4 rev/s, we can use the formula for centripetal force (F = mω²r) and equate it to the force due to gravity on the raised column of liquid to find the difference in height.
The angular velocity (ω) in this scenario would be the frequency (4 rev/s) times 2π (to convert to radians per second). Solving for the height difference yields approximately 4 cm, but this calculation assumes that the liquid adheres to simple physics models without taking complex fluid dynamics into account.