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Mechanical Properties of Solids

NCERT Class 11 Physics Chapter 8

Mechanical Properties of Solids for Class 11 Physics, JEE and NEET: stress, strain, Hooke’s law, stress-strain curve and Young’s, bulk and shear moduli.

7 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part II (Class 11), Chapter 8 “Mechanical Properties of Solids”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.2 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Elasticity and plasticity

    Elastic and plastic deformation, permanent set, and why steel is more elastic than rubber.

    NCERT Section 8.1 11 min read 3 solved examples 6 practice questions

  2. Stress and strain

    Stress = F/A, units and dimensions, longitudinal, shearing and hydraulic stress, with solved examples.

    NCERT Section 8.2 11 min read 4 solved examples 6 practice questions

  3. Hooke’s law

    Stress = k × strain, the modulus of elasticity, a wire as a spring, and where the law fails, with solved examples.

    NCERT Section 8.3 10 min read 4 solved examples 6 practice questions

  4. Stress-strain curve

    Proportional limit, yield point, ultimate strength, fracture, permanent set, brittle, ductile, elastomers.

    NCERT Section 8.4 13 min read 4 solved examples 6 practice questions

  5. Elastic moduli

    Young’s, shear and bulk modulus, compressibility, Poisson’s ratio and elastic energy, NCERT examples solved.

    NCERT Section 8.5 19 min read 6 solved examples 7 practice questions

  6. Experiment: Young’s modulus of a wire

    Searle’s apparatus, procedure, precautions, Y = MgL/(πrl), the load-extension graph and error analysis.

    JEE and NEET only 12 min read 3 solved examples 6 practice questions

  7. Applications of elastic behaviour

    How thick a crane rope must be, why beams have an I-section, pillars, and a simple estimate of mountain height.

    Class 11 only NCERT Section 8.6 13 min read 3 solved examples 6 practice questions

Key formulas in this chapter

Elasticity and plasticity

  • Restoring force = −(applied force) (body in equilibrium)
  • Fractional change in length = ΔL/L (ΔL = change in length, L = original length; no unit)
  • Permanent set = length after unloading − original length
  • F = −kx (spring, small extensions, up to the proportional limit)

Stress and strain

  • Stress = F/A (unit Pa, dimensions [MLT])
  • Longitudinal strain = ΔL/L
  • Shearing strain = Δx/L = tan θ ≈ θ
  • Volume strain = ΔV/V; hydraulic stress = p

Hooke’s law

  • Stress = k × strain (k = modulus of elasticity, in Pa)
  • F = −kx (spring; k = spring constant, in N m)
  • F = ks ΔL, ks = kA/L (wire of length L and cross-section A)

Stress-strain curve

  • Largest load without permanent set = σy × A
  • Maximum tensile load = σu × A (A = original area)
  • Permanent strain ≈ strain at C − (stress at C)/(slope of OA)

Elastic moduli

  • Y = σ/ε = FL/(AΔL)
  • G = (F/A)/(Δx/L) ≈ F/(Aθ) (small θ)
  • B = −p/(ΔV/V); compressibility k = 1/B
  • Poisson’s ratio = (Δd/d)/(ΔL/L) (Δd = diameter decrease)
  • W = ½Fl = YAl/(2L); u = ½σε

Experiment: Young’s modulus of a wire

  • Y = MgL/(πrl)
  • Y = gL/(πr × slope), slope = Δl/ΔM
  • ΔY/Y ≈ ΔL/L + 2Δd/d + Δl/l (first-order worst-case bounds; M and g exact)

Applications of elastic behaviour

  • A ≥ Mg/σy (rope or rod)
  • δ = Wl3/(4bd3Y) (beam loaded at the centre)
  • h ≈ (elastic limit of rock)/(ρg) (greatest mountain height)

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