Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Quick Summary
Properties of Matter covers the mechanical behaviour of solids (elasticity) and fluids (viscosity, surface tension, pressure). These topics connect to fluid mechanics in engineering and biology (blood flow, lung pressure).
Elasticity
Stress and Strain
| Term | Definition | Formula | Unit |
|---|---|---|---|
| Stress | Force per unit area | σ = F/A | Pa (N/m²) |
| Tensile strain | Fractional change in length | ε = ΔL/L | Dimensionless |
| Shear strain | Tangential displacement / height | γ = x/h | Dimensionless |
| Volumetric strain | Fractional change in volume | ΔV/V | Dimensionless |
Moduli of Elasticity
| Modulus | Definition | Formula |
|---|---|---|
| Young's modulus (Y) | Tensile stress / Tensile strain | Y = (F/A)/(ΔL/L) |
| Shear modulus (G) | Shear stress / Shear strain | G = (F/A)/(x/h) |
| Bulk modulus (B) | Volume stress / Volume strain | B = −P/(ΔV/V) |
Poisson's ratio: σ = Lateral strain / Longitudinal strain (0 < σ < 0.5 for most materials)
Hooke's Law
Within the elastic limit: stress ∝ strain
Viscosity
Newton's law of viscosity: F = η A (dv/dz)
η = coefficient of viscosity; SI unit: Pa s
Stokes' law: Drag force on a sphere = 6πηrv
Terminal velocity: v_t = 2r²(ρ − σ)g / 9η
Surface Tension
- Surface tension (T): Force per unit length = T = F/L; SI unit: N/m
- Excess pressure inside a bubble:
- Liquid drop: ΔP = 2T/r
- Soap bubble: ΔP = 4T/r (two surfaces)
- Capillary rise: h = 2T cosθ / (ρgr)
- Surface energy: Energy per unit area = T (same magnitude as surface tension)
Pressure in Fluids
- Pascal's law: Pressure applied to an enclosed fluid is transmitted equally in all directions.
- Pressure at depth h: P = P₀ + ρgh
- Archimedes' principle: Upthrust = weight of fluid displaced = ρ_fluid × V_submerged × g
- Bernoulli's theorem: P + ½ρv² + ρgh = constant (for ideal fluid flow)
Important Questions
One Mark
- State Hooke's law.
- Define Young's modulus.
- What is terminal velocity?
- State Pascal's law.
- Define surface tension.
Short Answer (3 marks)
- Explain stress and strain. Distinguish between three types of moduli of elasticity.
- Derive the expression for excess pressure inside a soap bubble.
- Explain capillary rise using the concept of surface tension. Derive the formula.
Long Answer (5 marks)
- Derive Stokes' law and the expression for terminal velocity of a sphere falling through a viscous medium.
- State and prove Bernoulli's theorem. Explain two applications: (a) Venturimeter, (b) aerofoil lift.
Common Mistakes
- Confusing soap bubble (4T/r) with liquid drop (2T/r) — soap bubble has two surfaces.
- Using Hooke's law beyond the elastic limit — it only applies within the proportional limit.
- Forgetting the negative sign in bulk modulus definition (compression increases pressure, decreases volume).
Board Exam Tips
- Excess pressure in drops and bubbles is a frequently tested 3-mark topic.
- Terminal velocity derivation using Stokes' law appears as a 5-mark question.
- Bernoulli's theorem applications are concept-based questions worth 3 marks.
Frequently Asked Questions
Hooke's law states that within the elastic limit, stress is directly proportional to strain. Stress ∝ Strain, so Stress = E × Strain, where E is the modulus of elasticity.