An open cylindrical vessel containing water rotates with constant angular speed 10 rad/s about its vertical axis. If the vessel radius is 0.20 m and g = 10 m/s², what is the difference between the free-surface heights at the rim and at the axis?
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Question

An open cylindrical vessel containing water rotates with constant angular speed 10 rad/s about its vertical axis. If the vessel radius is 0.20 m and g = 10 m/s², what is the difference between the free-surface heights at the rim and at the axis?

Options

G1 Physics · Accepted Answer

For a liquid rotating as a rigid body, the free surface is a paraboloid. The height difference between radius r and the axis is Δh = ω²r²/(2g). At the rim, r = 0.20 m. Therefore, Δh = 10²×0.20²/(2×10) = 100×0.04/20 = 0.20 m = 20 cm. Correct option: C.