MECHANICAL PROPERTIES OF SOLIDS
Complete NCERT Study Notes & 5-Part Mega Quiz for NEET
1. Elasticity and Plasticity
Elasticity: The property of a body by virtue of which it tends to regain its original size and shape when the applied force is removed. (e.g., steel, rubber).
Plasticity: The property where a body has no tendency to regain its previous shape and gets permanently deformed. (e.g., putty, mud).
2. Stress and Strain
Stress ($\sigma$): The restoring force developed per unit area of a deformed body.
$\text{Stress} = \frac{F}{A}$. Unit: $\text{N m}^{-2}$ or Pascal (Pa).
Strain ($\epsilon$): The fractional change in dimension produced in a body. It has no unit and no dimensions.
- Longitudinal Strain: $\frac{\Delta L}{L}$
- Shearing Strain: $\frac{\Delta x}{L} = \tan \theta \approx \theta$
- Volume (Hydraulic) Strain: $\frac{\Delta V}{V}$
3. Hooke's Law and Stress-Strain Curve
Hooke's Law: For small deformations, stress is directly proportional to strain. $\text{Stress} \propto \text{Strain} \implies \text{Stress} = k \times \text{Strain}$. Here $k$ is the Modulus of Elasticity.
- Proportional Limit: The region where Hooke's law is strictly obeyed (straight line).
- Yield Point (Elastic Limit): The point up to which the material remains elastic.
- Ultimate Tensile Strength: The maximum stress the material can withstand.
- Fracture Point: The point where the material breaks.
4. Elastic Moduli
Young's Modulus ($Y$): Ratio of longitudinal stress to longitudinal strain.
$Y = \frac{F/A}{\Delta L/L}$. Only solids possess Young's Modulus.
Shear Modulus or Modulus of Rigidity ($G$): Ratio of shearing stress to shearing strain.
$G = \frac{F/A}{\theta}$. Generally, $G \approx \frac{Y}{3}$.
Bulk Modulus ($B$): Ratio of hydraulic stress to corresponding volume strain.
$B = - \frac{P}{\Delta V/V}$. The negative sign shows that volume decreases with increasing pressure.
5. Poisson's Ratio & Elastic Potential Energy
Poisson's Ratio ($\sigma$): The ratio of lateral strain to longitudinal strain. It is a dimensionless number. For most metals, it lies between 0.2 and 0.33.
Elastic Potential Energy ($U$): The work done in stretching a wire is stored as potential energy.
Energy Density ($u$) = $\frac{1}{2} \times \text{Stress} \times \text{Strain} = \frac{1}{2} Y (\text{Strain})^2$.
🚀 NEET SOLIDS ELASTICITY MEGA QUIZ (100 MCQ)
Solve the 5 parts below to master Stress, Strain, Moduli, and Applications.
Post a Comment