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Hi! I want to clear my concepts regarding surface tension . This approach works well in case of a cylindrical tube but fails when the tube is conical. Why so? I tried this question by balancing the force of surface tension with the weight of water in the tube:
$$S(2πb)cos(θ+\frac{1}{2}α)=ρ(\frac{1}{3}πb²h)g$$
But my answer is wrong by using this approach. I know another approach to solve this question by balancing pressure. But I want to know what am I doing wrong in this, so that I can clear my concepts. Please help me.

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You have ignored the normal forces by the capillary tube, which balance the weight too alongside surface tension.

Hence you must first balance the pressure either to solve it directly or to find these normal forces

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