Mechanical Properties of Solids
Learn how solids respond to stretching, compression, pressure and shear with clear concepts, important formulas and JEE Main-focused problem-solving guidance.
The central idea of this chapter
Stress is the cause, strain is the deformation produced, and an elastic modulus measures how strongly a material resists that deformation. Keeping this chain clear makes most numerical questions easier.
What should you understand first?
Mechanical Properties of Solids connects force with deformation. The same external force can produce different deformation depending on area, length and material.
Core concepts
- Elasticity and plasticity High
- Stress and strain High
- Hooke's law High
- Stress–strain curve High
- Elastic potential energy Medium
Three deformation modes
- Change in length Young's Y
- Change in volume Bulk K
- Change in shape Shear G
- Wire extension FL/AY
- Energy density ½σε
Mechanical Properties of Solids formula sheet
Use the modulus that matches the type of deformation. Stress has the unit pascal, while strain is dimensionless.
| Topic | Formula / Relation | Meaning or use |
|---|---|---|
| Normal stress | σ = F / A | Normal force per unit cross-sectional area |
| Longitudinal strain | ε = ΔL / L | Fractional change in length |
| Young's modulus | Y = (F/A)/(ΔL/L) = FL/AΔL | Resistance to length deformation |
| Bulk modulus | K = −ΔP/(ΔV/V) | Resistance to volume change |
| Shear modulus | G = (F/A)/(Δx/L) | Resistance to shape deformation |
| Wire extension | ΔL = FL/(AY) | Extension of a uniform wire in elastic range |
| Elastic energy density | u = ½σε | Energy stored per unit volume |
Hooke's law and the stress–strain curve
Within the proportional region, stress is directly proportional to strain. Beyond the elastic limit, a body may not return completely to its original shape.
Important regions
- Linear region Y = slope
- Proportional limit Hooke's law ends
- Elastic limit Recovery limit
- Plastic region Permanent change
- Fracture point Breaking
How to read a question
- Length changes? Use Y
- Volume changes? Use K
- Shape changes? Use G
- Graph slope asked? Check axes
- Energy asked? Area / ½σε
How to prepare this chapter
Study in the order of cause, deformation, modulus and graph. This prevents mixing similar-looking formulas.
What to do
- Start with elasticity, stress and strain definitions
- Derive the wire-extension relation once
- Learn the roles of Y, K and G through deformation type
- Practise graph, energy and comparison questions
- Finish with chapter PYQs and a timed mock
Common mistakes
- Stress is not force; it is force divided by area
- Strain has no SI unit
- Do not use Young's modulus for volume change
- Check whether the graph is stress–strain or force–extension
- Remember the negative sign in bulk modulus convention
Ready to test your understanding?
Revise the formula sheet, then solve mixed JEE Main questions on wires, elastic energy and stress–strain graphs.
Mechanical Properties of Solids FAQ
Short answers to common JEE Main preparation questions.
Stress is the internal restoring force per unit area developed when an external force deforms a body. Normal stress is σ = F/A.
Young's modulus relates longitudinal stress to longitudinal strain. Bulk modulus relates volume stress to volumetric strain.
Yes. Strain is a ratio of similar quantities, such as ΔL/L, so it has no unit. It can be expressed as a percentage.
Understand stress and strain first, learn Hooke's law and the stress–strain curve, revise Y, K and G, and practise wire, graph and elastic-energy questions.