Surface Tension Explained Simply: Capillary Rise, Angle of Contact and MHT-CET Questions

A liquid surface behaves like a stretched elastic film. Molecules in the surface layer are pulled inward by their neighbours, so the surface shrinks to the smallest area it can and pulls along its edge. That pull per unit length is surface tension, and it acts tangentially to the free surface.

Which class is this? In Maharashtra the chapter, Mechanical Properties of Fluids, belongs to Standard XII (Std XII, the Class 12 year) and is Chapter 2 of the Balbharati Std XII Physics textbook. In Central Board of Secondary Education (CBSE) schools it is Class 11, NCERT Chapter 9, so CBSE readers can use our CBSE Class 11 physics chapters alongside. As of October 2026, the State Common Entrance Test Cell (CET Cell), which sets MHT-CET, lists the whole Std XII syllabus plus a named list of Std XI chapters, with about 20% Std XI and 80% Std XII weightage overall (page 1 of the CET Cell syllabus PDF). That split is by class, not chapter; our MHT-CET Physics syllabus guide explains it.

Cohesion, adhesion and the sphere of influence

Cohesion is attraction between molecules of the same liquid. Adhesion is attraction between different substances, such as water and glass. A molecule feels others only within its sphere of influence. Deep inside the liquid the pull is equal in all directions. In the surface film there are fewer liquid neighbours above than below, so the net pull is inward (Balbharati, section 2.4). The balance of adhesion and cohesion also sets the meniscus shape.

Surface tension T is the tangential force acting per unit length on an imaginary line drawn on a liquid's free surface, so T = F/L. Its SI (International System of Units) unit is N/m, which equals J/m². Its dimensions are [M L⁰ T⁻²]. Older books use dyne/cm: 1 N/m is 1000 dyne/cm.

In a question, use the T the question gives and say so; do not swap in the textbook value for water. A quick units and dimensions check confirms the form: N/m reduces to kg s⁻², with no length left in it.

Surface tension as surface energy: T = W/ΔA

Stretching a surface needs work, stored as surface energy. Take a wire frame holding a soap film, with a sliding wire of length l. The film has two surfaces, so the inward force on the wire is F = 2Tl. Pulling the wire out slowly through a distance x, at constant temperature, does work W = F·x = T(2lx) = T·ΔA, where ΔA = 2lx is the increase in the area of both surfaces (Balbharati, section 2.4.2). So T = W/ΔA, in J/m². Excess pressure inside drops and bubbles is a separate derivation, not covered here.

Temperature is the most predictable: surface tension falls as a liquid gets hotter. Impurities act both ways. Salt raises the surface tension of water, while phenol, detergent and insoluble impurities lower it. Soap is the standard example because it lowers T enough for water to soak into small pores.

Source: IAPWS Release R1-76(2014), Table 1, recommended values. Between 0.01 °C and 100 °C the value falls by 16.72 mN/m, about 22.1%. Balbharati (section 2.4.4) states the temperature and impurity effects, and the USGS notes that soaps and detergents lower surface tension so water soaks into pores. Balbharati's Table 2.1 lists a soap solution at 0.025 N/m at 20 °C, roughly a third of water's value.

The angle of contact is the angle between the tangent to the liquid surface and the solid surface at the point of contact, measured inside the liquid. An acute angle means the liquid wets the solid, the meniscus is concave and the liquid rises. An obtuse angle means a convex meniscus, and the liquid is pushed down.

At exactly 90°, cosθ = 0, the surface stays flat and h = 0.

For a tube of radius r dipped in a liquid of density ρ and surface tension T, with angle of contact θ, the height is h = 2T cosθ/(ρgr). A positive h is a rise. A negative h, which comes from a negative cosθ, is a fall below the outside level. Use the tube's radius, in metres.

Predict the rise or fall before you calculate

Ask whether θ is acute or obtuse: acute means expect a rise, obtuse a fall, and 90° no movement. Only then substitute. A negative h for water in clean glass means an error before the arithmetic.

Force balance behind the formula

Along the circle of contact, of length 2πr, the upward part of the surface tension force is 2πrT cosθ. It holds up the raised column, of weight πr²hρg, ignoring the small meniscus volume. Equating gives h = 2T cosθ/(ρgr). The textbook reaches the same result through the pressure difference across the curved surface (Balbharati, section 2.4.7).

In h = 2T cosθ/(ρgr), the height grows with T and cosθ and shrinks with ρ, g and r. Radius causes most mistakes, because data often arrives as a diameter or an area. Convert to radius first, then scale.

Diameter slip. A tube of diameter 0.6 mm has r = 0.3 mm. With the example's T = 0.07 N/m, θ = 0°, g = 9.8 m/s² and ρ = 1000 kg/m³, h = 2 × 0.07 ÷ (1000 × 9.8 × 0.0003) = 0.0476 m = 4.76 cm. Using 0.6 mm as r gives 2.38 cm, exactly half.

Tilted tube. If the vertical rise is 4 cm and the tube is held at 60° to the vertical, the liquid travels 4 ÷ cos 60° = 8 cm along the tube.

All four questions are original, and each tests one slip. Use the four-step numerical method for the working.

Q1: Area reduced to one-third (radius or area?)

Water rises 2.0 cm in a capillary tube. A tube of the same material with one-third the cross-sectional area replaces it. Find the new rise.

Solution: Area ∝ r², so the new radius is r/√3. Since h ∝ 1/r, h = 2.0 × √3 = 3.46 cm, about 3.5 cm.

Slip: Treating one-third as the ratio of radii gives 6.0 cm.

Q2: A capillary tube on the Moon

Water rises 2.5 cm in a capillary tube on Earth. The same tube and water are used on the Moon, where g is one-sixth of Earth's. Find the rise.

Solution: h ∝ 1/g, so a smaller g gives a larger h: 2.5 × 6 = 15 cm.

Slip: Dividing by 6 gives 0.42 cm.

Q3: Three liquids, same rise (which angle is larger?)

Liquids P, Q and R have densities 800, 1000 and 1200 kg/m³. Each has T = 0.05 N/m, and each rises 1.2 cm in a tube of radius 0.5 mm. Take g = 9.8 m/s² and arrange the angles of contact in increasing order.

Solution: From the formula, cosθ = hρgr/(2T). For the same rise, cosθ is proportional to density, so the denser liquid has the larger cosθ and the smaller angle. Numerically, cosθ = 0.470 for P, 0.588 for Q and 0.706 for R, giving θ = 61.9°, 54.0° and 45.1°. The order is θ_R < θ_Q < θ_P.

Slip: Reading the larger cosθ as the larger angle reverses the order.

Q4: Expanding a soap film (the two-surfaces factor)

A soap film on a wire frame is held by a sliding wire of length 8.0 cm. A force of 0.0048 N balances the film. Find T, then the work done in pulling the wire slowly a further 3.0 cm.

Solution: The film has two surfaces, so F = 2Tl and T = 0.0048 ÷ (2 × 0.080) = 0.030 N/m. The area increase is ΔA = 2 × 0.080 × 0.030 = 0.0048 m², so W = TΔA = 0.030 × 0.0048 = 1.44 × 10⁻⁴ J. Check: F·x = 0.0048 × 0.030 gives the same value.

Slip: Using ΔA = lx counts one surface and gives 7.2 × 10⁻⁵ J, half the right answer.

If you would rather work through this chapter with a teacher, see our MHT-CET Physics batches and check each batch page for what it covers.

Revise five formulas: T = F/L, T = W/ΔA, F = 2Tl for a soap film, h = 2T cosθ/(ρgr), and length along a tilted tube = h/cosα. Add one rule: fix the sign of cosθ, which tells you rise or fall, before any number goes in.

Practise previous years' questions (PYQ) with our chapter-wise PYQ plan.

This page stops at surface tension and capillary rise. Drops, bubbles, viscosity and Bernoulli’s principle complete the chapter and need their own revision.

Before your next practice set, run three checks: fix the sign of cosθ first, convert every diameter or area to a radius, and count both surfaces of a soap film. These three habits cover all four slips solved above.

Chapter weightage is historical, not official, so do not plan around a figure. The guide to chapter-wise weightage shows how to read any chapter figure you meet. Pair this page with regular PYQ practice, and revisit the three checks above before every test. Padhna Aasaan Hai.