Properties of Matter

Concept Core

Elasticity, viscosity, and surface tension — the three pillars of properties of matter.

Elasticity — Stress, Strain, and Young's Modulus

Stress = Force / Area (N/m²) Strain = Change in dimension / Original dimension (dimensionless) Young's Modulus Y = Tensile Stress / Tensile Strain = FL/(AΔL) Bulk Modulus K = Pressure / Volumetric Strain = −P/(ΔV/V) Modulus of Rigidity η = Shear Stress / Shear Strain

Hooke's Law: Stress ∝ Strain (within elastic limit). Beyond elastic limit → permanent deformation.

Elastic Energy Stored in a Wire

Energy U = ½ × Stress × Strain × Volume U = ½ × F × ΔL (since F = Y·A·ΔL/L) Energy density = ½ × Stress × Strain = Stress²/(2Y)

Viscosity — Stokes' Law

Viscous force (Stokes): F = 6πηrv Terminal velocity: vₜ = 2r²(ρ−σ)g / (9η) Poiseuille's Law: Q = πr⁴ΔP/(8ηL) (flow through pipe)

η = coefficient of viscosity (N·s/m²). Terminal velocity when weight = buoyancy + viscous drag. For liquids, η decreases with temperature. For gases, η increases with temperature.

Surface Tension

Surface tension T = Force / Length (N/m) Excess pressure inside bubble: ΔP = 4T/r (soap bubble, 2 surfaces) Excess pressure inside drop: ΔP = 2T/r (one surface) Capillary rise: h = 2T cosθ/(ρgr)

Soap bubble has 2 surfaces (inner and outer), hence 4T/r. Liquid drop has 1 surface, hence 2T/r.

Bernoulli's Equation & Continuity

Continuity: A₁v₁ = A₂v₂ (incompressible fluid) Bernoulli: P + ½ρv² + ρgh = constant Torricelli: v = √(2gh) (efflux from a hole)

Thermal Expansion

Linear: ΔL = αLΔT → L = L₀(1+αΔT) Area: ΔA = 2αAΔT (β = 2α) Volume: ΔV = 3αVΔT (γ = 3α) Relation: α : β : γ = 1 : 2 : 3

Formula Vault

Properties of matter formulas for EAPCET.

Young's Modulus

Y = FL/(AΔL)

F = force; L = length; A = area

Bulk Modulus

K = −PV/ΔV

Resistance to compression

Elastic Energy

U = ½ × F × ΔL = ½ × Stress × Strain × V

V = volume of wire

Stokes' Law

F = 6πηrv

η = viscosity; r = radius; v = speed

Terminal Velocity

vₜ = 2r²(ρ−σ)g/(9η)

ρ = sphere density; σ = fluid density

Surface Tension

T = F/l (N/m)

F = force along length l

Excess P in Soap Bubble

ΔP = 4T/r

Two surfaces → factor 4

Excess P in Drop

ΔP = 2T/r

One surface → factor 2

Capillary Rise

h = 2T cosθ/(ρgr)

θ = contact angle; r = tube radius

Thermal Expansion

α:β:γ = 1:2:3

Linear, area, volume coefficients

Worked Examples

5 problems — Young's modulus, terminal velocity, surface tension, Bernoulli, and a trap.

EasyFind extension of wire: Y=2×10¹¹ Pa, L=1m, A=10⁻⁶m², F=200N▾

A steel wire (Y = 2×10¹¹ N/m², L = 1 m, A = 10⁻⁶ m²) is loaded with F = 200 N. Find the extension.

Y = FL/(AΔL) → ΔL = FL/(YA)

ΔL = 200 × 1/(2×10¹¹ × 10⁻⁶) = 200/(2×10⁵) = 10⁻³ m = 1 mm

✓ Extension = 1 mm

EasyFind excess pressure inside a soap bubble of radius 5cm (T=0.03 N/m)▾

Find the excess pressure inside a soap bubble of radius 5 cm. Surface tension = 0.03 N/m.

Soap bubble (2 surfaces): ΔP = 4T/r = 4 × 0.03/(0.05) = 0.12/0.05 = 2.4 Pa

✓ Excess pressure = 2.4 Pa

MediumFind terminal velocity of sphere: r=0.5mm, ρ=8000 kg/m³, σ=1000 kg/m³, η=0.1 Pa·s▾

Find terminal velocity of a steel sphere (r = 0.5 mm, ρ = 8000 kg/m³) falling through oil (σ = 1000 kg/m³, η = 0.1 Pa·s). g = 10 m/s².

vₜ = 2r²(ρ−σ)g/(9η)

= 2×(0.5×10⁻³)²×(8000−1000)×10/(9×0.1)

= 2×2.5×10⁻⁷×70000/0.9 = 3.5×10⁻²/0.9 ≈ 0.039 m/s ≈ 3.9 cm/s

✓ Terminal velocity ≈ 3.9 cm/s

EAPCET LevelWater flows from radius 4cm pipe into radius 2cm pipe — find speed ratio▾

Water flows from a pipe of radius 4 cm into one of radius 2 cm. Find the ratio of speeds.

Continuity equation: A₁v₁ = A₂v₂

π(4)²v₁ = π(2)²v₂

16v₁ = 4v₂ → v₂/v₁ = 4

The smaller pipe has 4× higher speed.

✓ v₂ : v₁ = 4 : 1

Trap QuestionSoap bubble vs liquid drop — same formula for excess pressure?▾

A soap bubble and a liquid drop both have radius r = 2 cm, surface tension T = 0.04 N/m. Compare their excess pressures.

The trap: Same formula doesn't apply to both.

Soap bubble: 2 surfaces (inner and outer). ΔP = 4T/r = 4×0.04/0.02 = 8 Pa

Liquid drop: 1 surface (the outer surface only). ΔP = 2T/r = 2×0.04/0.02 = 4 Pa

Soap bubble has exactly double the excess pressure of a liquid drop of the same radius and surface tension.

✓ Soap bubble: 8 Pa; Drop: 4 Pa — bubble is double (two surfaces vs one)

Mistake DNA

3 properties of matter errors from EAPCET distractor analysis.

🫧

Using 2T/r for Soap Bubble (Should Be 4T/r)

A soap bubble has TWO surfaces (inner and outer), so the pressure formula is 4T/r, not 2T/r.

❌ Wrong

Soap bubble ΔP = 2T/r ✗ (one-surface formula; only valid for drop)

✓ Correct

Soap bubble: 4T/r ✓ (two surfaces contribute) Liquid drop: 2T/r ✓ (only outer surface)

Remember: soap film has inner and outer surfaces. Each contributes 2T/r. Total = 4T/r. A liquid drop has only one curved surface: ΔP = 2T/r.

🌡️

η of Liquids Increases with Temperature (Like Gases)

For liquids, viscosity DECREASES with temperature (molecules have more KE, layers slide more easily). For gases, η INCREASES with temperature.

❌ Wrong

Heating oil → more viscous (η increases) ✗ (that's for gases!)

✓ Correct

Liquids: η decreases with T ✓ (honey flows easier when warm) Gases: η increases with T ✓ (more molecular collisions)

Physical intuition: in liquids, viscosity arises from molecular attraction. Higher T → molecules overcome attraction → η decreases. In gases, viscosity arises from molecular momentum transfer between layers, which increases with T.

📐

α:β:γ = 1:2:3 Means β = 2 and γ = 3

The ratio is α:β:γ = 1:2:3, meaning β = 2α and γ = 3α. Not β = 2 and γ = 3 in absolute terms.

❌ Wrong

α = 12×10⁻⁶/°C → β = 2, γ = 3 ✗ (should be 2α, 3α)

✓ Correct

β = 2α = 24×10⁻⁶/°C ✓ γ = 3α = 36×10⁻⁶/°C ✓ The ratio is preserved not the absolute value

The thermal expansion coefficients maintain ratio 1:2:3 always. If linear expansion is α, area expansion is 2α and volume expansion is 3α.

Chapter Intelligence

Properties of matter integrates with fluids, thermal physics, and elasticity.

EAPCET Weightage (2019–2024)

Surface tension (bubbles, drops, capillary)

Young's modulus and stress/strain

Viscosity and terminal velocity

Bernoulli's equation

Thermal expansion α:β:γ

High-Yield PYQ Patterns

Excess pressure in soap bubble vs dropTerminal velocity calculationYoung's modulus extension of wireBernoulli: speed ratio in pipesCapillary rise heightα:β:γ = 1:2:3 propertyElastic energy in stretched wire

Exam Strategy

Soap bubble (2T/r each surface): ΔP = 4T/r. Liquid drop (1 surface): ΔP = 2T/r. The factor-of-2 difference is tested directly every few years.
Terminal velocity: all factors in the formula vₜ = 2r²(ρ−σ)g/(9η). Key insight: vₜ ∝ r² — doubling radius → 4× terminal velocity.
Thermal expansion: γ = 3α always. This is a direct fact question. Volume expands 3× more than linear for same ΔT.
Continuity equation: A₁v₁ = A₂v₂. Narrower pipe → faster flow. This is the basis of the Venturi meter and atomiser.

Concept Core

Formula Vault

Worked Examples

Mistake DNA

Chapter Intelligence

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