Physics notesFluids & WavesMatter props
Independent topic page
Tag the stem as surface/capillary, viscous drag, or Hookean elasticity in 15 seconds; one energy or force relation plus a unit check closes it.
01. Surface tension γ is force per unit length and also surface energy per unit area. Excess pressure inside a curved interface is set by geometry: 2γ/R for a liquid drop, 4γ/R for a soap bubble (two surfaces).
02. Angle of contact and capillary rise h=2γcosθ/(ρgr) encode wetting; meniscus shape follows whether the liquid wets the wall.
03. Viscosity η defines shear stress τ=η(dv/dx). Stokes drag on a sphere is in syllabus; laminar pipe Poiseuille flow is excluded—do not invent ΔP=8ηLQ/(πr⁴) on exam day.
04. Elasticity: stress/strain defines Young’s Y, rigidity η_mod (shear), and bulk B=−ΔP/(ΔV/V). Hooke’s law is the linear small-strain regime; energy density is ½×stress×strain.
05. Elasticity: match the modulus to the deformation—Y for longitudinal, η for shear, B for volume. Hooke is small-strain only; energy density is ½×stress×strain, not stress×strain.
06. Surface tension γ is force per length and energy per area. Excess pressure: 2γ/R for a drop, 4γ/R for a soap bubble (two surfaces). Capillary rise needs cosθ and tube radius.
07. Viscosity here is τ=η dv/dx or Stokes—pipe Poiseuille is outside the usual stem set unless explicitly built from first principles.
Official · 2026
Official syllabus points for Properties of Matter only — not the full Fluids & Waves portion map. Portion hub: Fluids & Waves · Fluid/Properties of Matter analysis.
No topic-specific exclusions flagged — finish the unit points below for Matter props.
Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf
Exam focusStress–strain, moduli, surface tension, and capillarity.
Syllabus points
2020–2026 paper weight
Topic match inside parent portion Fluid/Properties of Matter (2.1% of Physics tags). Stats below are portion backdrop; matched subtopics show where Properties of Matter sits.
No separate subtopic tag for Matter props — showing Fluid/Properties of Matter backdrop only.
Portion-wide type/difficulty mix lives on the Fluid/Properties of Matter analysis — not repeated here so this page stays on Matter props.
01. Fluid/Properties of Matter accounts for ~2.1% of tagged physics questions (2020–2026).
Full PCM trends board → · Fluid/Properties of Matter subject page →
Cross-topic stems
Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Properties of Matter — practise the knowledge bridge, not only the single-chapter drill.
No tagged mixed stem matched this topic’s keywords yet. Still revise the joins listed under Trends, and scan the mixed joins board for Mechanics / EM / Optics bridges.
Why methods matter
Stress–strain definitions and constraint expansions unify elasticity numericals.
Kills the classic 2γ/R vs 4γ/R trap instantly.
Do thisBefore ΔP or work, write one surface (drop) or two (soap film/bubble).
Kills the classic 2γ/R vs 4γ/R trap instantly.
Work to form soap bubble of radius R: two surfaces ⇒ W=8πR²γ (from 0 radius idealisation) or use ΔU=γΔA with ΔA=8πR².
Derives h without memorising sign errors; θ>90° gives depression.
Do thisVertical component 2πr γ cosθ = weight of raised column ρ(πr²h)g.
Derives h without memorising sign errors; θ>90° gives depression.
If cosθ<0, h is negative—liquid is depressed, not raised.
Prevents plugging shear data into Young’s formula.
Do thisMatch change in length → Y, angle/shape → rigidity, volume → B.
Prevents plugging shear data into Young’s formula.
Cube sheared by small angle φ: stress=η φ with φ≈Δx/L.
Matches Hookean linearity and catches factor-½ omissions.
Do thisFor stretch work, prefer U=½×stress×strain×volume over inventing average forces.
Matches Hookean linearity and catches factor-½ omissions.
Wire: U=½ (F/A)(ΔL/L)(AL)=½ F ΔL.
Processed examples
Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.
A wire of length 1 m and area 1 mm² stretches 1 mm under 100 N. Find Y.
This stem rewards early recognition of the young’s modulus and stress–strain model.
Model chosenY=(F/A)/(ΔL/L).
Answer10¹¹ Pa
Takeaway: Convert area to m² before dividing.
A liquid’s volume decreases by 0.1% under an extra pressure of 10⁶ Pa. Find the bulk modulus.
This stem rewards early recognition of the bulk and shear modulus model.
Model chosenB=ΔP/(−ΔV/V).
Answer10⁹ Pa
Takeaway: Bulk modulus uses fractional volume change.
A steel wire (Y=2×10¹¹ Pa) of length 2.0 m and area 1.0 mm² hangs vertically. A 5.0 kg mass is attached gently. Find the elastic energy stored.
This Advanced-level variation couples hidden constraints with the young’s modulus and stress–strain model.
Model chosenU=½FΔL with ΔL=FL/(AY).
Answer1.2×10⁻² J
Takeaway: Gradual loading stores ½FΔL, not FΔL.
Reusable models
Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.
Looks likeWire elongation, Y from load–extension
Fast modelY = (F/A)/(ΔL/L); energy = ½×stress×strain×volume.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeVolume compression or angle of shear
Fast modelB = −ΔP/(ΔV/V); η = shear stress / shear strain.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeWork to stretch a wire or spring-like rod
Fast modelU = ½ × stress × strain × volume = ½ F ΔL.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeBimetallic or rod with mismatch under load/temperature
Fast modelMechanical ΔL plus thermal ΔL must match constraints.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Hall timing
Underline given/asked quantities, free/closed surface labels, idealisations and the exact target. Reject any formula whose assumptions are already violated.
Write the governing relation symbolically before substitution; define a control volume, free body, reference level, or thermodynamic path if the stem mixes regimes.
Keep ratios and differentials exact as long as possible. Carry signs, gauge/absolute pressures, degrees of freedom and units on the rough sheet instead of repairing them later.
Check dimensions, limiting cases and physical sense. For multi-correct, test every option independently rather than forcing one common conclusion.
After the model is locked
γ=F/L; also γ=surface energy/area
Force on film or energy to create surface
ΔP=2γ/R (drop/air bubble in liquid); ΔP=4γ/R (soap bubble)
Curved interface pressure jump
h=2γcosθ/(ρ g r)
Narrow tube; θ=angle of contact
τ=η (dv/dx); F=ηA(dv/dx)
Laminar layers; definition of η
F=6πηrv
Small sphere, low Re (no Poiseuille)
Y=(F/A)/(ΔL/L)
Longitudinal stretch/compression
η=(F/A)/θ; B=−ΔP/(ΔV/V)
Shear angle θ; volume compression
U=½ F ΔL=½ (stress)(strain)(volume)
Hookean stored energy
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