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A glass capillary tube is shaped like a truncated cone, with its apex angle equal to alpha (so the tube wall makes an angle alpha/2 with the axis). The tube is held vertically and dipped in water, which rises to a height h where the tube's cross-sectional radius is b. The surface tension of water is S, its density is rho, and its contact angle with glass is theta. Taking g as gravitational acceleration, the expression for h is:
- 2S*cos(theta - alpha) / (b*rho*g)
- 2S*cos(theta + alpha) / (b*rho*g)
- 2S*cos(theta - alpha/2) / (b*rho*g)
- 2S*cos(theta + alpha/2) / (b*rho*g)
Correct answer: 2S*cos(theta + alpha/2) / (b*rho*g)
Solution
For a cylindrical tube the upward force per unit length is S*cos(theta). In a conical tube whose wall makes angle alpha/2 with the axis (vertical), the contact angle measured from the wall still equals theta, but the wall itself is already inclined by alpha/2 from the vertical. The net vertical component becomes S*cos(theta + alpha/2), giving h = 2S*cos(theta + alpha/2)/(b*rho*g).
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