Capillary rise: Class 11 practice
Liquid rises in a narrow tube to height h = 2S cos θ/(rρg), where S is surface tension and θ the contact angle (≈ 0° for water on clean glass). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Forces
- Density
The idea behind capillary rise
Liquid rises in a narrow tube to height h = 2S cos θ/(rρg), where S is surface tension and θ the contact angle (≈ 0° for water on clean glass). Narrower tubes give higher rise.
Step-by-step method
- Convert radius to m.
- Use h = 2S cos θ/(rρg).
- h ∝ 1/r for the same liquid.
Worked example 1 (Basic)
Water (S = 0.05 N/m, θ = 0°) rises in a tube of radius 0.2 mm. Find the height.
- h = 2 × 0.05/(0.0002 × 1000 × 9.8)
- Answer: 5.1 cm
Worked example 2 (Standard)
Water (S = 0.05 N/m, θ = 0°) rises in a tube of radius 0.9 mm. Find the height.
- h = 2 × 0.05/(0.0009 × 1000 × 9.8)
- Answer: 1.13 cm
Worked example 3 (Challenge)
Water rises 2.98 cm in a tube. How high will it rise in a tube with 4 times the radius?
- h ∝ 1/r
- Answer: 0.74 cm
Common mistakes and misconceptions
- Using diameter for r
- Forgetting cos θ
Practice questions
- (Basic) Water (S = 0.05 N/m, θ = 0°) rises in a tube of radius 0.8 mm. Find the height.
- (Basic) Water (S = 0.073 N/m, θ = 0°) rises in a tube of radius 0.2 mm. Find the height.
- (Standard) Water (S = 0.073 N/m, θ = 0°) rises in a tube of radius 0.6 mm. Find the height.
- (Standard) Water (S = 0.073 N/m, θ = 0°) rises in a tube of radius 0.7 mm. Find the height.
- (Challenge) Water rises 7.45 cm in a tube. How high will it rise in a tube with 2 times the radius?
- (Challenge) Water rises 2.1 cm in a tube. How high will it rise in a tube with 2 times the radius?
Answer key with full working
- Q1: h = 2 × 0.05/(0.0008 × 1000 × 9.8) → Answer: 1.28 cm
- Q2: h = 2 × 0.073/(0.0002 × 1000 × 9.8) → Answer: 7.45 cm
- Q3: h = 2 × 0.073/(0.0006 × 1000 × 9.8) → Answer: 2.48 cm
- Q4: h = 2 × 0.073/(0.0007 × 1000 × 9.8) → Answer: 2.13 cm
- Q5: h ∝ 1/r → Answer: 3.72 cm
- Q6: h ∝ 1/r → Answer: 1.05 cm
Syllabus note
This skill is listed under "Mechanical Properties of Fluids" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is capillary rise in?
"Mechanical Properties of Fluids", Class 11 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.