Water bubbles of radius R form at the bottom of a vessel and detach when the circular contact radius with the bottom is r. For r ≪ R, surface tension T and water density ρw, find r just before detachment. Image
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Question

Water bubbles of radius R form at the bottom of a vessel and detach when the circular contact radius with the bottom is r. For r ≪ R, surface tension T and water density ρw, find r just before detachment. 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 C: R²√(2ρw g/(3T)). Final answer: C.