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Surface Tension: Concepts, Formulas & Exam Practice Questions

🌊 Surface Tension: Concepts, Formulas & Exam Practice Questions

Author: Vivek Kumar | Category: Engineering Physics | Target Exams: SSC JE, RRB JE, PSU, State PSC

🔍 What is Surface Tension?

Surface tension is the property of a liquid surface that allows it to resist an external force due to cohesive nature of its molecules. It arises because molecules at the surface experience a net inward force, making the surface behave like a stretched elastic sheet.

🧠 Why It Matters in Competitive Exams?

Surface tension is a commonly tested topic in engineering exams under physics or fluid mechanics. Questions typically involve:

  • Conceptual understanding

  • Formula-based numerical problems

  • Application-based MCQs

📘 Key Concepts and Definitions

Concept Description
Cohesion Attraction between molecules of the same substance
Adhesion Attraction between molecules of different substances
Surface Tension (T or S) Force per unit length acting along the surface of a liquid in contact with another medium
Unit N/m or dyne/cm
Dimensional Formula [MT⁻²]
Capillarity Rise or fall of liquid in a narrow tube due to surface tension

📐 Important Formulas

  1. Surface Tension (T):

    T=FLT = \frac{F}{L}

    where
    FF = Force (N),
    LL = Length (m)

  2. Capillary Rise (h):

    h=2Tcos⁡θrρgh = \frac{2T \cos \theta}{r \rho g}

    where
    TT = surface tension,
    θ\theta = contact angle,
    rr = radius of capillary,
    ρ\rho = density of liquid,
    gg = acceleration due to gravity

  3. Excess Pressure inside a bubble:

    • Soap bubble (2 surfaces):

      P=4TrP = \frac{4T}{r}

    • Water droplet (1 surface):

      P=2TrP = \frac{2T}{r}

🌍 Real-World Examples

  • Water droplets forming spherical shapes

  • Insects walking on water

  • Capillary action in plants

  • Detergents lowering surface tension to clean more effectively

📝 Practice Questions with Answers

🔹 Conceptual MCQs

Q1. Which of the following units is used to measure surface tension?
A. N/m²
B. N/m
C. N
D. m/N
👉 Answer: B

Q2. When soap is added to water, the surface tension of water:
A. Increases
B. Decreases
C. Remains the same
D. Becomes infinite
👉 Answer: B

🔹 Numerical Questions

Q3. If the surface tension of water is 0.075 N/m and the radius of a droplet is 0.5 mm, what is the excess pressure inside the droplet?

Solution:

P=2Tr=2×0.0750.0005=300 PaP = \frac{2T}{r} = \frac{2 \times 0.075}{0.0005} = 300 \, \text{Pa}

👉 Answer: 300 Pa

Q4. In a capillary tube of radius 0.25 mm, water rises to a height of 5 cm. Calculate the surface tension. Assume:

  • ρ=1000 kg/m3\rho = 1000 \, kg/m^3,

  • g=9.8 m/s2g = 9.8 \, m/s^2,

  • θ=0∘\theta = 0^\circ

T=hrρg2cos⁡θ=0.05×0.00025×1000×9.82=0.06125 N/mT = \frac{hr\rho g}{2 \cos \theta} = \frac{0.05 \times 0.00025 \times 1000 \times 9.8}{2} = 0.06125 \, \text{N/m}

👉 Answer: 0.06125 N/m

🔹 Assertion and Reason

Q5.
Assertion (A): A drop of mercury is spherical.
Reason (R): Mercury has high surface tension.
A. A and R are true; R explains A
B. A and R are true; R does not explain A
C. A is true, R is false
D. A is false, R is true
👉 Answer: A

📌 Tips for Exam Preparation

✅ Focus on definitions, dimensional analysis, and formula-based numericals
✅ Understand how surface tension affects real-life applications
✅ Practice mixed question sets for quick revision
✅ Use diagrams to understand capillary action and droplets

📚 Related Topics

  • Viscosity

  • Fluid Mechanics

  • Capillarity

  • Thermodynamics of liquids


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