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A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is:

1. MLω² / 2
2. MLω²
3. MLω² / 2
4. MLω² / 2

Correct answer: MLω² / 2

Solution

The force at the other end is due to the centrifugal force acting on the liquid. The mass element at a distance x from the axis experiences a force proportional to x. Integrating this force over the length of the tube gives the total force as MLω² / 2.

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