More practice questions

4. Q4. In the tube of Example 1, hot water rises 5.45 cm instead of 5.90 cm. Taking the cold-water surface tension as 0.0723 N m^⁻¹ and ignoring the small change in density, find the surface tension of the hot water.

   Show answerHide answer

   At fixed r and ρ, S ∝ h, so S = 0.0723 × 5.45/5.90, about 0.067 N m^⁻¹. Surface tension falls as the temperature rises.

5. Q5. How high would water (S = 0.0727 N m^⁻¹) rise in a clean capillary of inner diameter 0.60 mm? Take g = 9.8 m s^⁻² and the density of water as 1000 kg m^⁻³.

   Show answerHide answer

   The radius is half the diameter, r = 0.30 mm. h = 2S/(ρgr) = 2 × 0.0727/(1000 × 9.8 × 0.30 × 10^⁻³), about 4.95 × 10^⁻² m, or about 4.9 cm. (Using the diameter by mistake would give half this rise.)

6. Q6. Why is the tube broken at the level of the meniscus to measure its radius?

   Show answerHide answer

   A real tube’s bore is not perfectly uniform. The radius that matters is the one at the meniscus, where surface tension acts, so it is measured there.