Rotate the Vessel

A liquid is kept in a cylindrical vessel, which is being rotated about its axis. The liquid rises at the side, as shown in the diagram.

If the radius of the vessel is \(0.05\text{ m}\) and the speed of rotation is \(2\) revolutions per second, find the difference in the heights of the liquid at the center of the vessel and its sides (in centimeters).

Take \(g = \pi^2 \text{ m/s}^2.\)

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