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A uniform capillary tube of inner radius r is inserted vertically into a beaker of water. Water rises to a height h inside the tube above the free surface in the beaker. The surface tension of water is S and the contact angle between water and the tube wall is theta. (Neglect the mass of the liquid in the meniscus.) Which of the following statements are TRUE?
- For a given tube material, h decreases as r increases
- For a given tube material, h is independent of S
- If the experiment is repeated in a lift accelerating upward at constant acceleration, h decreases
- h is proportional to the contact angle theta
Correct answer: For a given tube material, h decreases as r increases
Solution
From h = 2S*cos(theta)/(r*rho*g): (1) h is inversely proportional to r, so h decreases as r increases -- TRUE. (2) h depends on S -- FALSE. (3) In an upward-accelerating lift, g_eff = g+a increases, so h decreases -- TRUE. (4) h depends on cos(theta), not theta directly -- FALSE (h is proportional to cos(theta), not theta). Statements 1 and 3 are true.
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