Bihar Board - Class 11 physics - Chapter 9: Mechanical Properties of Solids Handwritten Notes

The chapter "Mechanical Properties of Solids" delves into how solids respond to external forces. It explores fundamental concepts like stress, strain, elastic modulus, and the behavior of materials under different conditions, offering insights into the strength and elasticity of solids.

Key Points

1. Stress and Strain

   • Stress: The restoring force per unit area within a material due to an external force. $$\text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{F}{A}$$ Types:
     • Tensile Stress: Stretching force.
     • Compressive Stress: Squeezing force.
     • Shear Stress: Tangential force.
   • Strain: The relative deformation experienced by a material. $$\text{Strain} = \frac{\Delta L}{L}$$Types:
     • Longitudinal Strain: Change in length.
     • Volumetric Strain: Change in volume.
     • Shear Strain: Angular distortion.

2. Hooke’s Law

   • Within the elastic limit, stress is directly proportional to strain: $$\text{Stress} \propto \text{Strain}, \quad \text{or} \quad \text{Stress} = E \cdot \text{Strain}$$ where $E$ = Elastic modulus.

3. Elastic Moduli

   • Measure of the material's elasticity. Types include:
     • Young’s Modulus ($E$): For longitudinal stress and strain. $$E = \frac{\text{Stress}}{\text{Strain}}$$
     • Bulk Modulus ($K$): For volumetric stress and strain. $$K = -\frac{\Delta P}{\frac{\Delta V}{V}}$$
     • Shear Modulus ($G$): For shear stress and strain. $$G = \frac{\text{Shear Stress}}{\text{Shear Strain}}$$

4. Elasticity and Plasticity

   • Elasticity: Ability of a material to regain its original shape after the removal of an external force.
   • Plasticity: Permanent deformation after the removal of force.

5. Stress-Strain Curve

   • Describes how a material behaves under stress. Key points:
     • Proportional Limit: Stress is proportional to strain.
     • Elastic Limit: Beyond this, permanent deformation occurs.
     • Yield Point: The material begins to deform plastically.
     • Breaking Point: Material fractures.

6. Applications of Elasticity

   • Springs: Governed by Hooke’s Law, used in mechanical devices.
   • Beams: Stress analysis for construction.
   • Bridges and Buildings: Elastic behavior ensures stability and durability.

7. Thermal Stress

   • Stress produced in a material due to temperature change: $$\Delta L = \alpha L \Delta T$$ where $\alpha$ = coefficient of linear expansion.

Conclusion

The chapter "Mechanical Properties of Solids" provides an essential understanding of how solids respond to forces, ensuring their safe and effective use in engineering and construction. Concepts like stress, strain, and elastic moduli are critical in designing materials and structures.

हिंदी के सभी अध्याय के महत्वपूर्ण प्रशन उत्तर के लिए अभी Download करें Vidyakul App - Free Download Click Here