Mechanical Properties of Solids – Complete Formula Sheet (JEE Main Only)
1. Elasticity – Basic Terms
- Stress (σ) = Force / Area
- Strain (ε) = Change / Original dimension
- Elastic limit → Max stress up to which Hooke’s law holds
- Plastic region → Permanent deformation
σ = F / A
ε = ΔL / L
2. Types of Stress & Strain
- Longitudinal stress (Tensile / Compressive)
- Shearing stress
- Bulk stress
- Longitudinal strain = ΔL / L
- Shear strain = θ (radian)
- Volumetric strain = ΔV / V
3. Hooke’s Law
Stress ∝ Strain
σ = Yε
τ = Gθ
P = K(ΔV / V)
4. Elastic Moduli
Young’s Modulus: Y = (FL) / (AΔL)
Bulk Modulus: K = −P / (ΔV / V)
Shear Modulus: G = τ / θ
5. Poisson’s Ratio
μ = Lateral strain / Longitudinal strain
- −1 ≤ μ ≤ 0.5
- Rubber → μ ≈ 0.5
6. Relations between Elastic Constants
Y = 2G(1 + μ)
Y = 3K(1 − 2μ)
G = Y / [2(1 + μ)]
K = Y / [3(1 − 2μ)]
7. Stress–Strain Curve
- Proportional limit
- Elastic limit
- Yield point
- Ultimate tensile stress
- Breaking point
8. Elastic Potential Energy
U = ½ (Stress × Strain × Volume)
U = ½ Yε²V
Energy density: u = ½ σε
9. Thermal Stress
If expansion is prevented:
σ = YαΔT
10. JEE Main Question Profiling (High-Value Section)
| Question Type | What JEE Main Tests | Common Trap |
|---|---|---|
| Direct formula MCQ | Y, K, G, μ substitution | Wrong relation between constants |
| Blocked expansion problems | Thermal stress concept | Ignoring σ = YαΔT |
| Energy density based | Conceptual + formula | Using total energy instead of density |
| Poisson ratio MCQ | Physical limits of μ | Assuming μ > 0.5 possible |
| Stress–strain curve | Material behavior | Confusing elastic & yield point |
| Shear deformation | Angle-based strain | Using degree instead of radian |
11. JEE Main Weightage Insight
- 1 guaranteed MCQ in most shifts
- Formula-based, low calculation load
- High scoring if traps avoided
StudyBeacon • JEE Main Physics • Exam-Profiled Notes
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