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A thin-walled capillary tube hangs vertically with its lower tip dipped a little into water in a cup. Before dipping, the cup was balanced on a beam balance. After the tube is dipped (water completely wets it and rises in the tube), the balance is restored by reducing the counter-weights by 0.14 g. If the surface tension of water is 0.07 N/m, find the radius r of the capillary (in mm).
- 1 mm
- 2 mm
- 0.5 mm
- 4 mm
Correct answer: 2 mm
Solution
Where the water wets the outer/inner contact line of the thin tube, surface tension pulls the tube down with force F = 2*pi*r*S (contact angle 0). Restoring balance required removing weight equivalent to this force: F = Δm*g. So 2*pi*r*S = 0.14e-3*9.8 → r ≈ 2 mm.
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