Mechanical Properties of Solids is Chapter 8 of NCERT Class 11 Physics and part of Unit 7, Properties of Solids and Liquids, in both the NEET UG and JEE Main syllabi. These notes cover stress and strain, Hooke’s law, the stress-strain curve, Young’s, shear and bulk moduli, Poisson’s ratio, elastic energy and applications, with a free PDF.
Mechanical Properties of Solids Notes for NEET and JEE Main
Section-wise key points from NCERT Chapter 8, comparison tables, high-yield facts and common mistakes for 2027 revision.
Mechanical Properties of Solids at a Glance
| Item | Details |
|---|---|
| NEET UG syllabus unit | Unit 7: Properties of Solids and Liquids |
| JEE Main syllabus unit | Unit 7: Properties of Solids and Liquids |
| Exams that cover it | Both NEET UG and JEE Main (Paper 1, B.E./B.Tech.) |
| NCERT textbook | Physics Part II, Class 11, Chapter 8 (rationalised book) |
| Other chapters in the unit | Mechanical Properties of Fluids (Chapter 9), Thermal Properties of Matter (Chapter 10) |
| Syllabus topics | Elastic behaviour; stress-strain relationship; Hooke’s law; Young’s modulus, bulk modulus and modulus of rigidity |
| Official chapter | NCERT Chapter 8 |
| Notes PDF | View PDF |
Topics follow the NEET UG 2026 syllabus released by the National Medical Commission (NMC) on 22 December 2025 and the JEE Main 2026 syllabus published by NTA. Both stay the reference until the 2027 syllabi are out. Full lists: NEET syllabus and JEE Main syllabus.
Elasticity and Plasticity
Elasticity is the property by which a body tends to regain its original size and shape when the deforming force is removed; plasticity is the absence of this tendency.
- No solid is perfectly rigid; even a steel bar deforms under a large enough force.
- A helical spring that returns to its length after being stretched shows elastic deformation.
- Putty and mud get permanently deformed and are close to ideal plastics.
- Knowledge of elastic behaviour is essential in designing buildings, bridges, automobiles, ropeways and artificial limbs.
Stress and Strain: Types and Units
Stress is the restoring force per unit area (F/A); strain is the fractional change in dimension. Stress has the SI unit N m⁻² or pascal (Pa) and dimensions [ML⁻¹T⁻²]; strain has no unit.
| Type of stress | How the force acts | Strain produced |
|---|---|---|
| Tensile or compressive (longitudinal) | Two equal forces normal to the cross-section, stretching or compressing | Longitudinal strain ΔL/L |
| Shearing (tangential) | Two equal and opposite forces parallel to opposite faces | Shearing strain Δx/L = tan θ ≈ θ |
| Hydraulic | Fluid pressure normal to the surface at every point | Volume strain ΔV/V, with no change in shape |
- The restoring force is equal in magnitude and opposite to the applied force.
- For θ = 10°, θ and tan θ differ by only about 1%, so tan θ ≈ θ for small shear.
- For a wire hung from a ceiling with weight F at its end, the tension at any cross-section is F, not 2F, so the stress is F/A.
- Stress is not a vector, because no single direction can be assigned to it.
Hooke’s Law and the Stress-strain Curve
Hooke’s law: for small deformations, stress is directly proportional to strain (stress = k × strain), where k is the modulus of elasticity. It is an empirical law.
| Region or point on the curve (metal) | What happens |
|---|---|
| O to A (proportional region) | Stress ∝ strain; Hooke’s law holds; the body regains its shape |
| A to B | Stress and strain not proportional, but the body still regains its shape |
| B: yield point (elastic limit) | Stress here is the yield strength σy |
| B to D (plastic region) | Strain rises quickly; on unloading the body keeps a permanent set |
| D: ultimate tensile strength | Maximum stress σu; beyond it strain grows even with less force |
| E: fracture point | The material breaks |
- Brittle material: D and E are close. Ductile material: D and E are far apart.
- Elastomers such as rubber and the elastic tissue of the aorta can be stretched to large strains, do not obey Hooke’s law over most of their elastic region and have no well-defined plastic region.
- Hooke’s law is valid only in the linear part of the curve.
Elastic Moduli: Young’s, Shear and Bulk
The ratio of stress to strain within the proportional region is the modulus of elasticity, a characteristic of the material.
| Modulus | Definition | Formula | Applies to |
|---|---|---|---|
| Young’s modulus Y | Tensile or compressive stress / longitudinal strain | Y = (F × L)/(A × ΔL) | Solids only |
| Shear modulus G (modulus of rigidity) | Shearing stress / shearing strain | G = (F × L)/(A × Δx) = F/(A × θ) | Solids only |
| Bulk modulus B | Hydraulic stress / volume strain | B = −p/(ΔV/V) | Solids, liquids and gases |
- All three moduli have the SI unit N m⁻² (Pa), the same as stress.
- Metals have large Young’s moduli. For 0.1% strain in a 0.1 cm² wire, steel needs 2000 N, while aluminium, brass and copper need 690 N, 900 N and 1100 N, so steel is preferred in heavy machines and structures.
- Wood, bone, concrete and glass have rather small Young’s moduli.
- For most materials G ≈ Y/3; the shear modulus is generally less than Young’s modulus.
- The minus sign in B shows that volume decreases as pressure increases; B itself is positive.
- Compressibility k = 1/B. Solids are the least compressible and gases the most; gases are about a million times more compressible than solids.
- A material that stretches less for a given load is more elastic; calling rubber ‘more elastic’ than steel is a misnomer.
Poisson’s Ratio and Elastic Potential Energy
NCERT also covers lateral strain and the energy stored in a stretched wire.
- Lateral strain is the strain perpendicular to the applied force (Δd/d for a wire).
- Poisson’s ratio = lateral strain / longitudinal strain = (Δd/d)/(ΔL/L). It is a pure number with no units.
- Poisson’s ratio is about 0.28 to 0.30 for steels and about 0.33 for aluminium alloys.
- Work done in stretching a wire is stored as elastic potential energy: U = ½ × Y × (strain)² × volume = ½ × stress × strain × volume.
- Elastic potential energy per unit volume: u = ½ σε.
Applications of Elastic Behaviour
Engineering design uses these ideas to keep loads within the elastic limit.
- Crane rope for a 10 tonne load: with mild steel yield strength about 300 × 10⁶ N m⁻², the radius must be at least about 1 cm; with a safety factor of about ten, a rope of about 3 cm radius made of many thin braided wires is used.
- Sag of a beam of length l, breadth b and depth d loaded at the centre: δ = Wl³/(4bd³Y). Increasing depth reduces bending more than increasing breadth.
- A deep beam can buckle, so load-bearing beams use an I-shaped cross-section, which saves weight without losing strength.
- A pillar with distributed ends supports more load than one with rounded ends.
- The maximum height of a mountain on earth is about 10 km, set by the elastic limit of rocks (about 30 × 10⁷ N m⁻²) against the shear due to the mountain’s weight.
Most-asked Facts for NEET and JEE Main: Mechanical Properties of Solids
Revise these one-line facts from the NCERT chapter just before the exam.
- Stress unit: N m⁻² or Pa; dimensions [ML⁻¹T⁻²]. Strain has no unit.
- Three types of stress: tensile or compressive, shearing and hydraulic.
- Hooke’s law holds only in the proportional (linear) region.
- Yield point is also called the elastic limit; its stress is the yield strength.
- Brittle: ultimate strength and fracture points close; ductile: far apart.
- Rubber and aortic tissue are elastomers.
- Y and G apply only to solids; B applies to solids, liquids and gases.
- G ≈ Y/3 for most materials.
- Compressibility is the reciprocal of bulk modulus.
- Steel is more elastic than copper, brass and aluminium.
- Poisson’s ratio has no unit; about 0.28 to 0.30 for steel.
- Elastic energy density u = ½ × stress × strain.
- Beam sag δ = Wl³/(4bd³Y); I-section beams resist bending and buckling.
- Maximum mountain height on earth ≈ 10 km.
Common Mistakes to Avoid
Watch for these mix-ups when you answer questions on this chapter.
- Calling rubber more elastic than steel because it stretches more. Steel is more elastic: it stretches less for the same load.
- Treating stress as a vector because force is a vector. Stress has no single direction.
- Taking the tension in a wire hung from a ceiling as 2F. It is F at every cross-section.
- Applying Young’s or shear modulus to liquids and gases. Only bulk modulus applies to fluids.
- Dropping the minus sign in B = −p/(ΔV/V) and getting a negative bulk modulus.
- Using Hooke’s law beyond the proportional limit, or for elastomers.
- Confusing the yield point with the ultimate tensile strength. Permanent set starts after the yield point; the maximum stress is at D.
- Giving strain or Poisson’s ratio a unit. Both are dimensionless ratios.
Mechanical Properties of Solids Notes PDF and Related Pages
Download the AglaSem notes for Mechanical Properties of Solids (key notes on properties of matter covering elasticity, surface tension and fluids, with important questions and answers) free: View PDF
- All chapters: NEET and JEE Main Physics notes
- Full topic lists: NEET syllabus and JEE Main syllabus
- Practice: NEET question papers and JEE Main question papers
- Source text: NCERT Chapter 8 (NCERT, Class 11 Physics Part II)
Physics Notes for NEET and JEE Main: All Chapters
- Units and Measurement
- Motion in a Straight Line
- Motion in a Plane
- Laws of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermodynamics
- Kinetic Theory of Gases
- Oscillations
- Waves
- Thermal Properties of Matter
- Electric Charges and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Electromagnetic Waves
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics
All chapters with key points and notes PDFs are on the Physics notes for NEET and JEE Main page.
Mechanical Properties of Solids Notes for NEET and JEE Main FAQs
Which NCERT chapter is Mechanical Properties of Solids?
It is Chapter 8 of the rationalised NCERT Class 11 Physics textbook, the first chapter of Part II. It falls under Unit 7, Properties of Solids and Liquids, in both the NEET UG 2026 and JEE Main 2026 syllabi.
Is Mechanical Properties of Solids in the NEET and JEE Main 2027 syllabus?
Yes. Elastic behaviour, the stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus and modulus of rigidity are in both syllabi. These remain the reference until the 2027 syllabi are released.
Which elastic modulus applies to liquids and gases?
Only the bulk modulus. Young’s modulus and shear modulus need a definite length and shape, which only solids have.
What is the difference between a brittle and a ductile material?
On the stress-strain curve, a brittle material has its ultimate tensile strength point and fracture point close together, so it breaks soon after yielding. A ductile material has them far apart and can be drawn out before breaking.
Are these notes enough for this chapter?
No. Read NCERT Chapter 8 first, then use these notes and the PDF for revision, and practise numerical problems on Young’s modulus and bulk modulus from previous year papers.