A centrifuge has a horizontal cylinder rotating about a vetical axis as shown in the figure. Water inside it has density `rho`.
(a) Consider a point A. Inside the liquid, at a distance r from the rotation axis. Liquid pressurea t his point is P. Write the value of `(dP)/(dr)` when the cylinder, with all its liquid. rotates uniformly at an angular speed `omega`.
(ii) Consider a small disc shaped foreign material inside the centrifuge at point A. The area of circular disc is `DeltaS` and its thickness is `Deltar`. It disc is in position so that its circular face is vertical. Find the radial acceleration of the disc with respect to the cylinder when angular speed of rotation is

Answer

(a) `(dP)/(dr)=rhoomega^(2)r`
(b) `(1-(rho)/(rho))omega^(2)r`