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.
1
Y = FL/(AΔL) → ΔL = FL/(YA)
2
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.
1
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.
2
= 2×(0.5×10⁻³)²×(8000−1000)×10/(9×0.1)
3
= 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.
1
Continuity equation: A₁v₁ = A₂v₂
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.
1
The trap: Same formula doesn't apply to both.
2
Soap bubble: 2 surfaces (inner and outer). ΔP = 4T/r = 4×0.04/0.02 = 8 Pa
3
Liquid drop: 1 surface (the outer surface only). ΔP = 2T/r = 2×0.04/0.02 = 4 Pa
4
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)~7 Young's modulus and stress/strain~6 Viscosity and terminal velocity~5 Thermal expansion α:β:γ~3 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.