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Elasticity

NEET > Physics > Properties of Bulk Matter

Unit Progress

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Overview content

Chapter Snapshot - Elasticity

Elasticity covers the behaviour of solids under deforming forces — from interatomic forces holding matter together to the mathematical moduli that quantify how materials stretch, compress, and shear. You will learn stress, strain, Hooke's law, three elastic moduli (Young's, Bulk, Rigidity), Poisson's ratio, elastic potential energy, and practical consequences like breaking stress, elastic fatigue, and applications in engineering structures.

✓ Use This To Plan Your First 2–3 Hours
Expected Questions (Typical)
Q
2-3
NEET typically tests Young's modulus calculations (wire stretching), energy stored in a wire, and conceptual facts about elasticity comparisons (steel vs rubber, hollow vs solid shaft).
Time Required (Practical)
⏱
6-8 hrs
Theory and derivations take ~3 hrs; numerical practice (Y, K, η problems) takes ~3 hrs; MCQ revision another 1-2 hrs.
Difficulty Level
⚡
Moderate
Formula-based numericals are straightforward once Y = FL/AΔl is internalised. Conceptual traps around steel-vs-rubber elasticity and Poisson's ratio limits need extra attention.
Most Asked Style: Numerical — given load, length, radius of wire, find elongation or Young's modulus. Also frequent: 'energy stored in stretched wire' and 'which material is more elastic' conceptual questions.Biggest Trap: Confusing 'more elastic' with 'easier to stretch' — steel has a HIGHER Young's modulus than rubber and is therefore MORE elastic, not less.Fast Win: Memorise U = ½Fl (energy stored in wire) and Y = FL/AΔl with unit substitutions; these two formulae appear in ~60% of all elasticity questions.Revision-Friendly: The stress-strain curve landmarks (P = proportionality limit, E = elastic limit, B = breaking point) are a one-diagram revision of the entire chapter's qualitative content.

Subtopics - Elasticity (NEET)

From interatomic bonds to engineering beams — master the science of deformation

Revision tip: Draw the stress-strain curve from memory first. Then hang all formulae (Y, K, η, σ, U) off it — proportionality limit for Y, elastic limit for fatigue, plastic region for breaking stress.
NCERT LinesMCQsQuick Test

1) Stress and Strain

Definitions, types, units, and the stress-strain curve. Covers interatomic/intermolecular forces, elasticity vs plasticity, elastic limit, elastic fatigue, elastic after-effect, and all three types of stress and strain.

Normal StressShear StressLinear StrainVolumetric StrainShearing StrainStress-Strain CurveHooke's Law
›
Interatomic and Intermolecular ForcesNature of interatomic forces (r₀ = equilibrium distance), F = −dU/dr, intermolecular Vander Waal forces, comparison table.
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Elasticity and PlasticityDefinitions of elasticity, plasticity, perfectly elastic body (quartz, phosphor bronze), perfectly plastic body (paraffin wax, wet clay), elastic limit.
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Elastic Fatigue and After-EffectElastic fatigue = temporary loss of elasticity after repeated stress cycles; elastic after-effect = time delay in regaining shape after removal of deforming force.
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Types of StressNormal stress (longitudinal: tensile/compressive; bulk/volumetric) and shear/tangential stress. Dimensions [ML⁻¹T⁻²], units N/m².
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Types of StrainLinear strain = Δl/l (longitudinal + lateral); volumetric strain = ΔV/V; shearing strain φ = x/L. All dimensionless.
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Stress-Strain CurveOPE: elastic region; OP: Hooke's law region (proportionality limit P); E: elastic limit; EABC: plastic region; B: ultimate tensile strength (breaking point).

2) Elastic Moduli — Y, K and η

Three moduli of elasticity corresponding to three strain types. Young's modulus for wires/rods, Bulk modulus for volume changes (with compressibility), and Modulus of Rigidity for shearing. Breaking stress, energy stored in stretched wire, and torsion of cylinders.

Young's ModulusBulk ModulusModulus of RigidityCompressibilityBreaking StressElastic PETorsion
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Young's ModulusY = (F/A)/(Δl/L) = FL/AΔl. For wire: Y = MgL/πr²l. Force constant k = YA/L. Elongation by own weight = MgL/2AY.
›
Work Done and Elastic PEU = ½Fl = ½ × stress × strain × volume. Energy per unit volume Uᵥ = ½Y(strain)² = (stress)²/2Y.
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Breaking Stress and Safety FactorBreaking force ∝ area; breaking stress independent of dimensions. Maximum length before breaking: L = P/dg. Safety factor = breaking stress / working stress.
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Bulk Modulus (K)K = −pV/ΔV. Compressibility C = 1/K. Isothermal elasticity E₀ = P; adiabatic elasticity Eφ = γP. K_solid > K_liquid > K_gas.
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Modulus of Rigidity (η)η = shear stress/shear strain = (F/A)/φ. Only for solids. In torsion: C = πηr⁴/2l; work done W = ½Cθ².

3) Poisson's Ratio and Elastic Constants

Lateral vs longitudinal strain, Poisson's ratio definition and limits, volumetric strain relation, and the interconnecting relations between Y, K, η and σ. Interatomic force constant and elastic hysteresis.

Poisson's RatioLateral StrainY–K–η RelationsInteratomic Force ConstantElastic Hysteresis
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Poisson's Ratio (σ)σ = −(dr/r)/(dL/L). Theoretical range: −1 < σ < 0.5; practical range: 0 < σ < 0.5. σ = 0.5 → incompressible; σ = 0 → cork-like (max volume change).
›
Volumetric Strain RelationdV/V = (1 − 2σ)dL/L. Relates volumetric strain to longitudinal strain and Poisson's ratio.
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Relations Between Elastic ConstantsY = 3K(1 − 2σ); Y = 2η(1 + σ); Y = 9Kη/(3K + η); σ = (3K − 2η)/(6K + 2η).
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Interatomic Force ConstantK = F/Δr = Y × r₀ (where r₀ = equilibrium interatomic distance). Unit N/m, dimension MT⁻².
›
Elastic HysteresisStrain lags behind stress during loading/unloading. Area of hysteresis loop = work done per loading-unloading cycle. Rubber B (small loop) for tyres; Rubber A (large loop) to absorb vibrations.

4) Practical Properties and Applications

Comparing elasticity of materials, practical engineering applications, factors that affect elasticity (hammering, annealing, temperature, impurities), hollow vs solid shafts, beam depression, and maximum mountain height.

Steel > RubberFactors Affecting ElasticityHollow Shaft > Solid ShaftBeam DepressionTorsion Applications
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Comparing ElasticitySteel is more elastic than rubber (higher Y). Ivory > Steel > Rubber > Clay. K_solid > K_liquid > K_gas. Rigid body: Y, K, η → ∞.
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Moduli Values for MaterialsSteel: Y = 20×10¹⁰ N/m², K = 16×10¹⁰ N/m², η = 8.4×10¹⁰ N/m². Diamond and carborundum nearest to rigid bodies.
›
Factors Affecting ElasticityHammering/rolling → increase elasticity; Annealing → decrease elasticity; Temperature rise → decrease elasticity (exception: invar steel); Impurities → may increase or decrease.
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Hollow Shaft vs Solid ShaftHollow shaft is stronger than solid shaft of same mass, length, material: τ_hollow/τ_solid = (r_S² + r_I²)/r² > 1.
›
Beam Depression and ApplicationsRectangular beam: δ = Wl³/4Ybd³. Increasing depth > breadth minimises depression → I-shaped girder. Maximum mountain height: h_max = K/ρg. Bridges declared unsafe due to elastic fatigue.

Elasticity Download Notes & Weightage Plan

For each topic in the Elasticity chapter below, you get (2) the exact resources to download and how to use them, and (3) a simple importance & time plan so NEET students know what to do first and what to revise last.

2 Downloads

Stress and Strain

Understanding what happens inside a material when an external force deforms it — the internal restoring force per area (stress) and the fractional change in configuration (strain).

Normal StressShear StressLinear StrainVolumetric StrainHooke's LawStress-Strain Curve

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)Stress = F/A, unit N/m², dimension [ML⁻¹T⁻²]. Three stress types: longitudinal (tensile/compressive), bulk, shear. Three strain types: linear (Δl/l), volumetric (ΔV/V), shearing (φ = x/L) — all dimensionless. Stress-strain curve: OP (proportional), E (elastic limit), B (breaking point). Elastic limit = property of body; elasticity = property of material. Elastic fatigue: bridges made unsafe; spring balances give wrong readings. Elastic after-effect: glass > quartz (quartz has negligible after-effect).
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Draw the full stress-strain curve free-hand with all landmark labels (P, E, A, B, C). Then write the three stress definitions and three strain formulae. Do 5 numerical questions on identifying stress type from a given scenario.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Usually conceptual — 'which stress type' or 'which is more elastic'.
Time Required1.5 hrs30 min theory, 30 min stress-strain curve practice, 30 min MCQs.
DifficultyEasy-ModerateDefinitions are straightforward; traps arise in comparing elasticity of materials.
  • Scoring Focus: Elastic fatigue and after-effect facts; stress-strain curve landmarks; steel > rubber misconception.
  • High-risk Area: Students say rubber is more elastic than steel because it stretches more — the opposite is true (higher Y = more elastic).
  • Best Practice Style: Conceptual + assertion-reason questions.
Priority rule: Cover before moduli — everything else depends on understanding stress and strain first.

Elastic Moduli — Y, K and η

Quantifying elastic behaviour through three moduli. Young's modulus for longitudinal deformation of wires and rods, Bulk modulus for volumetric compression, and Modulus of Rigidity for shear deformation.

Y = FL/AΔlK = −pV/ΔVη = F/AφU = ½FlCompressibility = 1/KBreaking Stress

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)Y = FL/AΔl = MgL/πr²l (wire). For same force: elongation ∝ L/r². Elongation by own weight = MgL/2AY = L²dg/2Y. U = ½Fl = ½ × stress × strain × volume. Uᵥ = ½Y(strain)² = (stress)²/2Y. Breaking force ∝ A; breaking stress constant for material; L_max = P/dg. K = −pV/ΔV; C = 1/K; isothermal: E₀ = P; adiabatic: Eφ = γP. η = (F/A)/φ — solids only. Torsion constant C = πηr⁴/2l.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Start with Y = FL/AΔl and derive force constant k = YA/L. Practice 10 numericals varying F, L, r, and asking for Δl. Memorise energy table (total U vs per-unit-volume Uᵥ). Then do bulk modulus problems on density change of compressed liquid.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions1-2Mostly numerical — elongation, Y from experiment, energy stored in wire. NEET 2018, 2019 both had wire-stretching questions.
Time Required2.5 hrs1 hr derivations + 1.5 hrs numericals.
DifficultyModerateFormula application is systematic; hardest part is choosing correct area formula and not mixing up U and Uᵥ.
  • Scoring Focus: Y = MgL/πr²l with correct substitution; U = ½Fl directly from data; K and compressibility conceptual comparison.
  • High-risk Area: Using wrong area (πr² vs πd²/4); forgetting negative sign in K; confusing isothermal vs adiabatic elasticity for gases.
  • Best Practice Style: Multi-step numericals with two wires compared for elongation, or given Y to find energy stored.
Priority rule: Highest priority in the chapter — 70% of elasticity marks come from Young's modulus problems.

Poisson's Ratio and Elastic Constants

How stretching in one direction affects the other directions (Poisson's ratio), the theoretical and practical limits, and the inter-relations connecting all four elastic constants.

σ = lateral/longitudinal strain−1 < σ < 0.5Y = 3K(1−2σ)Y = 2η(1+σ)K = Ya (interatomic)

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)σ = −(dr/r)/(dL/L), dimensionless. Theoretical: −1 < σ < 0.5; practical: 0 < σ < 0.5. dV/V = (1−2σ)dL/L. σ = 0 → cork (no lateral change, max ΔV); σ = 0.5 → incompressible (ΔV = 0, K = ∞). Relations: Y = 3K(1−2σ); Y = 2η(1+σ); Y = 9Kη/(3K+η); σ = (3K−2η)/(6K+2η). Interatomic force constant K = Y×r₀ (unit N/m). Elastic hysteresis: strain lags behind stress; area of loop = energy dissipated.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Memorise the two primary relations Y = 3K(1−2σ) and Y = 2η(1+σ). Use them to derive the combined formula Y = 9Kη/(3K+η). Practice 3-4 MCQs on finding σ given Y and K or η.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Usually one formula-based question on Y-K-η relation or a conceptual question on Poisson's ratio limits.
Time Required1 hr30 min theory + 30 min MCQ practice.
DifficultyModerateRelations are easy to memorise but often confused under exam pressure.
  • Scoring Focus: Y = 9Kη/(3K+η) and the special cases of σ = 0 and σ = 0.5.
  • High-risk Area: Getting the sign wrong in σ = (3K−2η)/(6K+2η); confusion about which limit (theoretical vs practical).
  • Best Practice Style: Short formula-based MCQs; conceptual true/false about incompressible materials.
Priority rule: Medium priority — memorise the two main relations, skip detailed proofs.

Practical Properties and Applications

Engineering uses of elasticity principles — comparing materials, factors affecting elasticity, hollow shafts vs solid shafts, beam depression, and maximum mountain height estimation.

Steel > Rubber (elastic)K_solid > K_liquid > K_gasHollow > Solid ShaftBeam δ ∝ 1/d³h_max = K/ρg

1) Download Packs For This Topic (And How To Use Them)

Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.

↓
Topic Notes (Condensed)More elastic = higher modulus (not easier to stretch). Y and η only for solids; K for all states. Rigid body → moduli = ∞. Hammering/rolling → ↑ elasticity; annealing → ↓ elasticity; temperature rise → ↓ elasticity (invar exception); impurities → variable. Hollow shaft stronger: τ_hollow > τ_solid (same mass). Beam depression δ = Wl³/4Ybd³; increase depth > breadth → use I-section girder. Max mountain: h_max = K/ρg. Bridges unsafe due to elastic fatigue of ropes under repeated loading.
Download NotesPrintable PDF
★
NCERT Key Lines (One-Liners)These are the lines NEET converts into "statement is correct/incorrect" questions.
NCERT LinesFlashcards
Q
Practice Set (MCQs + PYQs)Do 30–50 questions, then mark errors as "memory miss" or "confusion between options."
MCQ SetPYQs
How to revise: Make a 2-column table: situation → elastic modulus involved (e.g., automobile tyre → K; automobile shaft → η; suspension bridge ropes → Y). Review important facts list from pages 457-458 for quick MCQ answers.

2) Importance, Weightage & Time Allocation (Practical)

Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.

Expected Questions0-1Usually a factual/application question — which modulus applies, or comparing heights of balls after bouncing.
Time Required1 hr45 min reading factual notes + 15 min quick-fire MCQs.
DifficultyEasyMostly recall-based; no complex calculations.
  • Scoring Focus: Application-to-modulus mapping; hollow vs solid shaft comparison; steel more elastic than rubber.
  • High-risk Area: Thinking bulk modulus is only for gases (it applies to all states); forgetting that Young's modulus and η exist only for solids.
  • Best Practice Style: Application-based single-line MCQs and statement-based questions.
Priority rule: Low-medium priority for numericals; high priority for quick fact-based MCQs in last-minute revision.

Elasticity Chapter NEET Traps & Common Mistakes (Topic-Wise)

Each subtopic below is of the Elasticity chapter and shows what NEET students usually do wrong in NEET examination, a short example of the mistake, and how NEET frames the question to trick you with close options are given below.

! Avoid Easy Negatives
Steel vs Rubber Elasticity
Young's ModulusElasticity DefinitionCommon Misconception

Mistake Snapshot (What Students Do Wrong)

  • Rubber = more elastic: Students equate 'stretches more for same force' with 'more elastic' — this is the opposite of the correct definition.
  • Ignoring Y values: Steel Y ≈ 20×10¹⁰ N/m² >> Rubber Y ≈ 0.05×10¹⁰ N/m²; steel resists deformation far more per unit stress.
2–3 Line Example (Typical Error)

Identical loads hung on steel wire (Δl = 0.1 mm) and rubber wire (Δl = 50 mm) — steel is more elastic because it showed less deformation.

How NEET Frames The Trap

NEET options often list 'rubber is more elastic' as option (a) to trap students who conflate flexibility with elasticity.

NEET-Style Trap Question Format

Q. For the same deforming force, a rubber wire stretches 500 times more than a steel wire of the same dimensions. Which statement is correct?
A. Rubber is more elastic than steel   B. Steel is more elastic than rubber   C. Both have the same elasticity   D. Elasticity cannot be compared for different materials  
Trick: More elastic = higher modulus = less deformation for same stress. Steel deforms less → steel MORE elastic.

Quick rule: Greater deformation for same force = LESS elastic. Steel has higher Y → MORE elastic than rubber.
Energy Stored in Stretched Wire
Elastic PEU = ½FlUnit Volume Energy

Mistake Snapshot (What Students Do Wrong)

  • U = Fl instead of ½Fl: Forgetting the ½ factor — elastic PE is analogous to a spring: U = ½kx², not kx².
  • Confusing total U and Uᵥ: Total U = ½ × stress × strain × volume; per unit volume Uᵥ = ½ × stress × strain. Students forget to multiply or divide by volume.
2–3 Line Example (Typical Error)

Wire of length 2 m, cross-section 1 mm², Y = 2×10¹¹ N/m², stretched 1 mm by force F. Energy = ½ × F × 0.001 J — not F × 0.001 J.

How NEET Frames The Trap

Questions often give force and elongation and ask for 'work done' — the answer is ½Fl, not Fl (which would be energy if dissipated, not stored elastically).

NEET-Style Trap Question Format

Q. When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + l). The elastic potential energy stored in the extended wire is [NEET 2019]
A. Mgl   B. MgL   C. ½Mgl   D. ½MgL  
Trick: Work done by gravity = Mgl, but elastic PE stored = ½Fl = ½Mgl. The ½ comes because force builds up from 0 to Mg as the wire stretches.

Quick rule: U_stored = ½ × (final force) × (elongation) = ½Fl. Always half the product.
Breaking Stress vs Breaking Force
Breaking StressBreaking ForceWire Dimensions

Mistake Snapshot (What Students Do Wrong)

  • Breaking stress depends on length: Breaking stress is constant for a given MATERIAL — it is independent of length AND thickness of wire.
  • Breaking force constant for same material: Breaking force = Breaking stress × Area: it depends on cross-sectional area, not length. Larger area → larger breaking force.
2–3 Line Example (Typical Error)

A wire can hold 500 N. Cutting it in half: each half still holds 500 N (breaking stress unchanged). Doubling diameter → breaking force becomes 4× = 2000 N.

How NEET Frames The Trap

MCQs ask 'if a wire is cut into 3 equal pieces, what load can each piece hold?' — answer is the same as original (breaking stress × same area).

NEET-Style Trap Question Format

Q. A rope 1 cm in diameter breaks when tension exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is:
A. 250 N   B. 500 N   C. 1000 N   D. 2000 N  
Trick: Breaking force ∝ A ∝ r². Diameter doubles → area quadruples → breaking force = 4 × 500 = 2000 N.

Quick rule: Breaking STRESS = constant for material (size-independent). Breaking FORCE = stress × area (proportional to r²).
Poisson's Ratio Limits
Poisson's RatioTheoretical vs PracticalIncompressible Material

Mistake Snapshot (What Students Do Wrong)

  • Wrong limits: Theoretical range is −1 < σ < 0.5; practical range is 0 < σ < 0.5. Negative σ is theoretically possible but not practically observed.
  • σ = 0.5 means zero Young's modulus: σ = 0.5 means K → ∞ (incompressible), not Y = 0; it corresponds to ΔV = 0 when stretched.
2–3 Line Example (Typical Error)

Cork has σ ≈ 0 (no lateral change when compressed — why it seals bottles). Rubber has σ ≈ 0.5 (nearly incompressible).

How NEET Frames The Trap

Assertion-reason MCQs claim 'Poisson's ratio cannot exceed ½' — TRUE for practical materials, but theoretical allows up to 0.5 (not exceeded).

NEET-Style Trap Question Format

Q. For a material with Poisson's ratio σ = 0.5, when a rod is stretched along its length:
A. Volume increases significantly   B. Volume remains essentially unchanged   C. Length decreases   D. Radius increases  
Trick: dV/V = (1 − 2σ)dL/L = (1 − 2×0.5)dL/L = 0. Volume stays constant → material is incompressible.

Quick rule: σ = 0.5 → incompressible (ΔV = 0, K = ∞). σ = 0 → maximum volume change (cork). Range: 0 < σ < 0.5 practically.

Topics

Interatomic and Intermolecular Forces

States of Matter and Types of Solids

Elastic Properties of Matter

Hooke's Law and Modulus of Elasticity

Important Facts and Practical Applications

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NEET > Physics > Properties of Bulk Matter Chapters

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Elasticity

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Surface Tension

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Fluid Mechanics

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Thermometry, Thermal Expansion and Calorimetry

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