A glass capillary tube is a truncated cone with apex angle α. When dipped vertically in water, the rise is h at a location where tube radius is b. With surface tension S, liquid density ρ and contact angle θ, find h. Image
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Question

A glass capillary tube is a truncated cone with apex angle α. When dipped vertically in water, the rise is h at a location where tube radius is b. With surface tension S, liquid density ρ and contact angle θ, find h. Image

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G1 Physics · Accepted Answer

Step 1: Use surface-energy/pressure relations: ΔP = 2T/R for a liquid drop or 4T/R for a soap bubble, capillary rise h = 2T cosθ/(ρgr), and surface energy = TΔA. Step 2: Apply force or energy balance to the stated radii and surface areas. Applying these relations to the given data gives D: (2S/(bρg)) cos(θ+α/2). Final answer: D.