Capillarity and Contact Angle - UNSOLVED PRACTICE SET

Q7. Define capillarity. Explain why water rises in a capillary tube while mercury is depressed.

Q8. Derive the expression for the height of capillary rise in a tube of radius r.

Q9. A capillary tube of radius 0.2 mm is dipped in water. Calculate the height of water rise. (Surface tension of water = 7 × 10⁻² N/m, density = 1000 kg/m³, g = 9.8 m/s², angle of contact = 0°)

Q10. In your school, a student notices that ink spreads quickly on blotting paper. Explain this using capillarity.

Q11. Why does water rise higher in a thinner capillary tube? Is there a limit to how high it can rise?

Q12. The angle of contact for a liquid-solid pair is 120°. Will the liquid rise or be depressed in a capillary tube made of this solid? Explain.

Q13. Explain the phenomenon of capillarity. Derive the expression for capillary rise (or depression) in a tube of radius r. Discuss the role of:

(i) Surface tension

(ii) Angle of contact

(iii) Density of liquid

(iv) Radius of tube

Explain why water rises in a glass capillary while mercury is depressed.

Q14. Two capillary tubes of radii 0.5 mm and 1 mm are dipped vertically in water.

(a) Calculate the height of water rise in each tube. (T = 7 × 10⁻² N/m, θ = 0°, ρ = 1000 kg/m³)

(b) Calculate the excess pressure inside each meniscus.

(c) If the tubes are dipped in a liquid of surface tension 4 × 10⁻² N/m and density 800 kg/m³, calculate the new heights.

(d) Discuss why farmers plough their fields before the rainy season.

(e) Explain how capillary action helps in the movement of water in plants.

Q15. Analyse the following situations:

(i) A drop of water on a lotus leaf forms a nearly spherical bead

(ii) A drop of mercury on glass forms a nearly spherical bead

(iii) Water spreads on clean glass but forms beads on a greasy surface

For each case, explain:

(a) The angle of contact

(b) The relative strengths of cohesive and adhesive forces

(c) The practical significance

Q16. A capillary tube of radius 0.4 mm is dipped vertically in water. The tube is held so that its lower end is 2 cm below the water surface and its upper end is 5 cm above the water surface.

(a) Calculate the height to which water rises in the tube.

(b) What is the shape of the meniscus at the top of the water column?

(c) If the tube is now lowered until only 1 cm is above the water surface, what happens?

(d) Calculate the pressure at the top of the water column in each case.

(e) Discuss why the water does not flow out of the top of the tube.

Q17. In a school experiment, students investigate capillary rise in tubes of different radii.

(a) Design an experiment to verify that capillary rise is inversely proportional to tube radius.

(b) Water rises to heights of 4 cm, 2 cm, and 1 cm in three tubes. Calculate the ratio of their radii.

(c) If the largest tube has radius 0.5 mm, calculate the surface tension of water from the data.

(d) A student uses a tube of radius 2 mm and observes no noticeable rise. Explain why.

(e) Suggest how to modify the experiment to measure surface tension of mercury.

Q18. A towel hangs with its lower end dipped in a bucket of water. After some time, the entire towel becomes wet.

(a) Explain this phenomenon using capillarity.

(b) If the towel fibres can be modelled as capillary tubes of radius 0.05 mm, calculate the maximum height water can rise. (T = 7 × 10⁻² N/m, θ = 0°)

(c) Why does water continue to rise even above this calculated height in a real towel?

(d) Explain why synthetic towels dry faster than cotton towels using surface tension concepts.

(e) Discuss how this principle is used in oil lamps and kerosene stoves.