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A U-tube of cross-sectional area S holds two immiscible liquids of densities rho and 2*rho whose interface is at point A. The total liquid column above A is of height 8a/3, where AB = a. The tube is rotated about a vertical axis located at distance a, with angular speed omega. Find omega such that the interface moves from A towards B by 2a/3.
- sqrt(2g/(5a))
- sqrt(3g/(7a))
- sqrt(g/(3a))
- sqrt(5g/(2a))
Correct answer: sqrt(3g/(7a))
Solution
The centrifugal effect raises pressure in the outer arm, displacing the heavier liquid and shifting the interface by 2a/3. Equating the static height difference produced to the centrifugal pressure term gives omega in terms of g and a. (This subjective problem has been cast with constructed options containing the computed result.)
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