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A liquid fills a vertical tube whose cross-section is a semicircle (a diameter plus a semicircular arc). The contact angle is zero. Find the ratio of the surface tension force acting on the curved (arc) portion of the perimeter to that acting on the flat (diameter) portion.
- 1: 1
- 1: 2
- pi: 2
- 2: pi
Correct answer: pi: 2
Solution
With zero contact angle, the surface tension force on a boundary length L is F = T*L. The semicircular cross-section perimeter has two parts: the curved arc of length pi*r and the straight diameter of length 2r. Ratio of forces = (T*pi*r)/(T*2r) = pi: 2.
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