Elasticity & Viscosity: JEE Main Physics Guide

Elasticity and viscosity are compact chapters that JEE Main tests with one to two questions per session. They are conceptually straightforward but formula-dense, and the key to scoring here is accurate recall of the relationships between stress, strain, moduli, and flow parameters. A focused three-hour session on both chapters is enough to lock in the marks they offer.

Stress, Strain, and Hooke's Law

Stress = Force/Area (N/m² = Pa). Strain = Change in dimension/Original dimension (dimensionless). Hooke's Law states that stress is proportional to strain within the elastic limit: stress = modulus × strain. The three elastic moduli are: Young's modulus Y = (F/A)/(ΔL/L) = FL/(AΔL) for longitudinal deformation; Bulk modulus K = −V(dP/dV) for volumetric deformation under pressure; Shear modulus (Rigidity modulus) G = (F/A)/(x/h) for shear deformation. JEE Main tests all three through direct calculation and conceptual questions about which modulus applies to which type of deformation.

Poisson's ratio σ = −(lateral strain)/(longitudinal strain). For an incompressible material, σ = 0.5. Practically, σ lies between 0 and 0.5. The relation between elastic moduli: Y = 3K(1−2σ) = 2G(1+σ). JEE Main occasionally asks you to use these inter-modulus relations. Elastic potential energy stored per unit volume = ½ × stress × strain = stress²/(2Y). For the related chapter on fluid statics, see our Fluid Mechanics Guide.

Stress-Strain Curve

The stress-strain curve for a ductile material has several key points: proportional limit (Hooke's law holds up to here), elastic limit (material returns to original shape if stress removed), yield point (permanent deformation begins), ultimate tensile strength (maximum stress), and fracture point. JEE Main tests the identification of these regions and the comparison between ductile and brittle materials — brittle materials fracture near the elastic limit without significant plastic deformation.

Viscosity and Fluid Flow

Viscosity η is the property of a fluid that resists flow. Viscous force F = ηA(dv/dy), where dv/dy is the velocity gradient perpendicular to flow. Unit of η: Pa·s (SI) or poise (CGS), with 1 Pa·s = 10 poise. Temperature dependence: viscosity of liquids decreases with temperature; viscosity of gases increases with temperature. JEE Main tests this temperature dependence comparison regularly.

Stokes' law: viscous force on a sphere moving through a fluid = 6πηrv. Terminal velocity: v_t = 2r²(ρ_sphere − ρ_fluid)g/(9η). JEE Main asks to calculate terminal velocity for a sphere falling through oil or glycerine — plug into the formula directly. Take a free mock test that includes elasticity and viscosity questions to test your recall under time pressure.

Poiseuille's Equation and Reynolds Number

Volume flow rate through a cylindrical pipe: Q = πr⁴ΔP/(8ηL), where ΔP is the pressure difference across length L. This is Poiseuille's equation. Note the fourth-power dependence on radius — doubling the pipe radius increases flow rate by a factor of 16. JEE Main tests this scaling relationship in the form of ratio problems.

Reynolds number Re = ρvd/η classifies flow: Re < 1000 gives laminar flow, Re > 2000 gives turbulent flow. JEE Main uses Reynolds number conceptually — asking whether flow becomes turbulent when velocity increases, or which parameter change causes the transition.

Surface Tension Connection

Surface tension is treated alongside elasticity in many textbooks — the surface of a liquid behaves like an elastic membrane under tension. Surface energy per unit area = surface tension T (N/m). Excess pressure inside a soap bubble = 4T/r; inside a liquid drop = 2T/r. Capillary rise h = 2T·cosθ/(ρgr). For a complete treatment of surface tension and capillarity, see our Surface Tension Guide.

Revision Strategy

Make a single formula table with all three moduli, Stokes' law, Poiseuille's equation, and terminal velocity. Every year, one question can be answered by reading this table. The other question will test conceptual understanding — the stress-strain curve or temperature-viscosity relationship. Two hours on this chapter converts to 4-8 marks with high reliability. For a structured revision timeline, see our 30-Day Physics Plan. Upgrade for ₹149/month for chapter-wise mock tests with detailed solutions.