Hooke’s law defines the proportional relationship between stress and strain within the elastic limit.
Hooke’s law defines the proportional relationship between stress and strain within the elastic limit.
The CBSE syllabus for 2024-2025 includes Chapter 8 “Mechanical Properties of Solids” from the Class 11 NCERT Physics textbook. This chapter explores key concepts like stress, strain, elasticity, Young’s modulus, bulk modulus, shear modulus and Poisson’s ratio. It describes the behavior of solids under various forces and the factors influencing their mechanical properties. Multiple-choice questions help evaluate understanding of fundamental principles such as Hooke’s Law and stress-strain relations. Mastery of these concepts is essential not only for academic success but also for practical applications in fields such as engineering and material science.
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Hooke’s Law
Hooke’s Law is a principle of physics that describes the behavior of elastic materials when subjected to forces. It states that the deformation (strain) of an elastic object is directly proportional to the force (stress) applied to it, provided the material’s elastic limit is not exceeded.
Mathematical Expression:
Hooke’s Law is expressed mathematically as:
\[
F = -kx
\]
Where:
– **F** is the force applied to the object (in newtons, N).
– **k** is the spring constant or stiffness of the material (in N/m), which measures the object’s resistance to deformation.
– **x** is the displacement or deformation of the object from its equilibrium position (in meters, m).
Key Points:
1. **Proportionality:** The force and displacement are proportional; doubling the displacement doubles the force, as long as the material stays within its elastic limit.
2. **Elastic Limit:** Beyond a certain point, called the elastic limit, the material will no longer obey Hooke’s Law. Permanent deformation or failure may occur.
3. **Negative Sign:** The negative sign in the formula indicates that the force exerted by the material is in the opposite direction of the displacement, representing a restoring force.
Applications of Hooke’s Law:
– **Springs:** Used to calculate forces in springs and other elastic systems.
– **Engineering:** Applied in structural analysis and material science to determine stress and strain in materials.
– **Oscillations:** Forms the basis for analyzing simple harmonic motion in oscillatory systems.
Limitations:
– Hooke’s Law is valid only for materials and forces within the elastic region.
– It does not apply to materials that exhibit plastic deformation or other non-linear behaviors.
Understanding Hooke’s Law is essential for various fields of physics and engineering, as it provides a foundation for studying elasticity and material behavior.
This question related to Chapter 8 physics Class 11th NCERT. From the Chapter 8. Mechanical Properties of Solids. Give answer according to your understanding.
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https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/