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Schooling · Class 11 · Physics · Mechanical Properties of Solids · Chapter on a page

CBSE Class 11 · Physics · NCERT Physics Part-II

Mechanical Properties of Solids: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

Mind map of Mechanical Properties of Solids: Key ideas, Formulas and facts, Worked examples, Watch out forKey ideasStressStrainHooke's lawElastic limitYoung's modulus (Y)Bulk modulus (B)Shear modulus or rigidity modulus (G)Formulas and factsStress = Force / Area = F/A (unit…Longitudinal strain = Change in…Volume strain = Change in volume /…Shear strain = Angular displacement…Y = (F × L) / (A × ΔL)Bulk modulusG = (F/A) / θWorked examplesCalculating Young's modulusFinding bulk modulusEnergy stored in a stretched wireWatch out forForgetting to convert millimetres to…Treating strain as having a unitUsing positive sign for volume…Confusing tensile stress with shear…Assuming Hooke's law applies for any…MechanicalProperties of Solids
The mind map as a list
  • Key ideas
    • Stress
    • Strain
    • Hooke's law
    • Elastic limit
    • Young's modulus (Y)
    • Bulk modulus (B)
    • Shear modulus or rigidity modulus (G)
  • Formulas and facts
    • Stress = Force / Area = F/A (unit…
    • Longitudinal strain = Change in…
    • Volume strain = Change in volume /…
    • Shear strain = Angular displacement…
    • Y = (F × L) / (A × ΔL)
    • Bulk modulus
    • G = (F/A) / θ
  • Worked examples
    • Calculating Young's modulus
    • Finding bulk modulus
    • Energy stored in a stretched wire
  • Watch out for
    • Forgetting to convert millimetres to…
    • Treating strain as having a unit
    • Using positive sign for volume…
    • Confusing tensile stress with shear…
    • Assuming Hooke's law applies for any…

What this chapter is about

This chapter explores how solid materials respond when external forces act on them. When you stretch a rubber band, compress a spring, or twist a metal rod, the material changes shape. The study of these deformations and the forces that cause them forms the core of this chapter.

Key ideas

  • Stress is the internal restoring force per unit area developed inside a material when an external force deforms it. Unit: N/m² or pascal (Pa). Stress = F/A.
  • Strain is the fractional change in dimension (length, volume or shape) produced by stress. It is a ratio and has no unit.
  • Hooke's law states that within the elastic limit, stress is directly proportional to strain. The constant of proportionality is called the modulus of elasticity.
  • Elastic limit is the maximum stress up to which a material returns to its original shape after the deforming force is removed; beyond this, permanent deformation occurs.
  • Young's modulus (Y) measures resistance to longitudinal (tensile or compressive) deformation: Y = longitudinal stress / longitudinal strain = (F/A) / (ΔL/L). Unit: Pa.
  • Bulk modulus (B) measures resistance to uniform volume change under pressure: B = volume stress / volume strain = −ΔP / (ΔV/V). The negative sign accounts for decrease in volume with increase in pressure.
  • Shear modulus or rigidity modulus (G) measures resistance to shape change at constant volume: G = shear stress / shear strain = (F/A) / θ, where θ is the angle of shear in radians.
  • Poisson's ratio (σ) is the ratio of lateral strain to longitudinal strain; it lies between 0 and 0.5 for most materials.

Formulas and facts to remember

  • Stress = Force / Area = F/A (unit: Pa or N/m²).
  • Longitudinal strain = Change in length / Original length = ΔL/L (no unit).
  • Volume strain = Change in volume / Original volume = ΔV/V (no unit).
  • Shear strain = Angular displacement θ (in radians) ≈ tan θ for small angles.
  • Young's modulus: Y = (F × L) / (A × ΔL).
  • Bulk modulus: B = −ΔP / (ΔV/V) = −P × V / ΔV.
  • Shear modulus: G = (F/A) / θ.
  • Elastic potential energy stored per unit volume = (1/2) × stress × strain = (1/2) × Y × (strain)².

Common mistakes

  • Forgetting to convert millimetres to metres before substituting into formulas → always express all lengths in SI units (metres).
  • Treating strain as having a unit → strain is a ratio of two lengths (or volumes) and is dimensionless.
  • Using positive sign for volume change under compression → volume decreases, so ΔV is negative; the negative sign in the bulk modulus formula keeps B positive.
  • Confusing tensile stress with shear stress → tensile stress acts perpendicular to the cross-section; shear stress acts parallel (tangential) to the surface.
  • Assuming Hooke's law applies for any size of load → it holds only within the elastic limit; beyond that, the material behaves plastically.

Quick revision

  • Stress = F/A; strain = fractional change in dimension; both share the same formula structure but stress has unit Pa, strain has none.
  • Hooke's law: stress ∝ strain within elastic limit.
  • Y for length change, B for volume change, G for shape change.
  • Elastic energy per unit volume = (1/2) × stress × strain.
  • Poisson's ratio links lateral and longitudinal strains; it lies between 0 and 0.5.
  • Beyond the elastic limit, materials undergo permanent (plastic) deformation.