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A horizontal tube of length L is completely filled with an incompressible liquid of total mass M and sealed at both ends. It is rotated in a horizontal plane about one of its ends with constant angular velocity omega. What is the force exerted by the liquid on the closed end farthest from the axis of rotation?

1. M*omega²*L/2
2. M*omega²*L
3. M*omega²*L/4
4. 3*M*omega²*L/4

Correct answer: M*omega²*L/2

Solution

Each element of the rotating liquid requires a net inward (centripetal) force. The pressure at the far closed end multiplied by the cross-section equals the total centripetal force needed for the whole column, which is found by integrating over all elements.

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