Surface Tension & Capillarity: JEE Main Guide

Surface tension is a classic chapter where every formula arises from a single physical idea: the surface of a liquid minimises its area because surface molecules are pulled inward by net cohesive forces. Once you understand this, every result — excess pressure in drops, capillary rise, detergent behaviour — follows without memorisation. JEE Main tests this chapter with one to two questions per session, mostly numerical.

Surface Tension: Definition and Units

Surface tension T is defined as the force per unit length acting on any imaginary line drawn on the liquid surface, perpendicular to the line. T = F/L; units: N/m. Equivalently, T equals the surface energy per unit area (J/m²). The two definitions are numerically identical since N/m = J/m². JEE Main frequently asks: "which quantity equals surface tension?" and the answer is both force per unit length AND energy per unit area.

Temperature decreases surface tension (hot liquids spread more easily). Dissolved impurities: soap and detergents lower surface tension, enabling them to penetrate fabric fibres. Pure dissolved salts increase surface tension slightly. JEE Main tests these qualitative trends. For the related topic of viscosity and fluid flow, see our Elasticity & Viscosity Guide.

Excess Pressure Inside Curved Surfaces

Excess pressure inside a liquid drop = 2T/r. Excess pressure inside a soap bubble = 4T/r (factor of 2 because soap film has two surfaces). Excess pressure inside an air bubble in liquid = 2T/r (one surface). JEE Main asks these three results in quick-fire form — the most common error is applying the soap bubble formula to a liquid drop. The rule: count the number of surfaces and multiply 2T/r by that count.

When two soap bubbles of radii r₁ and r₂ are connected by a thin tube, the smaller bubble (higher internal pressure) collapses into the larger. Resultant radius R: 4T/R = 4T/r₂ − 4T/r₁ (if r₂ > r₁), giving 1/R = 1/r₂ − 1/r₁. Take a free mock test including surface tension problems to practise applying these pressure formulas.

Angle of Contact and Wetting

The angle of contact θ is measured through the liquid between the tangent to the liquid surface and the solid surface at the point of contact. θ < 90° (acute): liquid wets the solid, meniscus is concave (water in glass). θ > 90° (obtuse): liquid does not wet the solid, meniscus is convex (mercury in glass). θ = 0° means complete wetting. Adding detergent to water decreases θ, making water wet more surfaces.

Capillary Rise and Fall

Capillary rise h = 2T·cosθ/(ρgr). For water in glass (θ ≈ 0°, cosθ = 1): h = 2T/(ρgr). Capillary rise is inversely proportional to radius — thinner tubes give higher rise. For mercury in glass, θ > 90° so cosθ < 0, meaning h is negative — mercury is depressed in the capillary rather than raised. JEE Main tests both rise and depression scenarios in the same question by asking for the sign of h.

Jurin's law: h·r = constant for a given liquid-solid system. Doubling the radius halves the height. This is a ratio question pattern JEE Main uses frequently — if a capillary of radius r gives rise h, what rise does radius 2r give? Answer: h/2. The weight of liquid lifted = 2πrT·cosθ (the upward force equals weight at equilibrium).

Energy Methods in Surface Tension

Work done in blowing a soap bubble of radius r: W = 8πr²T (surface area = 8πr² for two surfaces). Work done in splitting a drop of radius R into n drops of radius r: each small drop has r = R/n^(1/3). Total surface area increases, so work must be done. ΔW = T × (increase in surface area) = T × [4πr² × n − 4πR²] = 4πT(nr² − R²). These energy calculations appear in JEE Main's numerical-answer section.

Exam Strategy

Surface tension questions reward careful formula recall. Make a card with: T = F/L = surface energy/area, excess pressures (1×, 2×, 4× for air-liquid-soap bubble), capillary rise formula, and the two wetting behaviours. Review it daily for one week. Link this chapter with our Fluid Mechanics Guide for the broader fluid physics picture. Upgrade for ₹149/month for topic-level chapter tests with 80+ surface tension problems.