Physics Spl

Poisson's Ratio (? ) is used when a material is subjected to axial stress. It is the ratio of lateral strain to longitudinal strain. Mathematically, it is:

Derivation of the Poisson Ratio includes when a material is stretched, its width decreases (called lateral strain) and its length increases which is called longitudinal strain.

Poisson's Ratio (? ) is a dimensionless quantity and it is normally between a range of 0 to 0.5 for most materials. It is used in engineering applications including for bridge and building design. It is used in analyzing the structural deformations. Materials like rubber which has a high Poisson's ratio when stretched, exhibit significant lateral expansion.

According to the NCERT Solutions for Class 11 Physics Chapter 8 Mechanical Properties of Solids, when an external force is applied to a solid, the solid undergoes changes in shape or size which is called deformation. The solid deformation can be classified into:

Elastic Deformation: It is when the body returns to its original size and shape after the force is removed. It occurs within the elastic limit and follows Hooke's law. The most common examples include stretching a helical spring or a rubber band.

Plastic Deformation: It occurs beyond the elastic limit and here after the removal of the force, the body does not return to its original shape and size. Hence, the force applied leads to the permanent deformation of the solid. Common examples include deformation in putty, clay or bending of a metal wire beyond a certain limit.

The plastic deformation is irreversible and elastic deformation is reversible. These concepts are important when studying engineering, material science, and construction.

The modulus of elasticity refers to the material's capacity to withstand or resist deformation when stress is applied. There are three types of the modulus of elasticity including:

Young's Modulus (E): It is used to measure a solid's elasticity when longitudinal stress (tensile or compressive) is applied to it. Mathematically, it is represented by the following formula;

SI Unit is N/m² (Pascal, Pa).

Bulk Modulus (K): It is used to measure the ability of the material to resist volume change when uniform pressure is applied to it. Mathematically, it is:

SI Unit is N/m² (Pa)

Shear Modulus (G) or Modulus of Rigidity: It is used when a shear force is applied to measure the resistance to shape change. Mathematically, it is represented by:

SI Unit: N/m² (Pa)

The value of each modulus varies for different materials, and it describes different types of deformation.

The chapter consists of fundamental topics that are important for board exams preparation as well as for competitive tests: 

• Composition and Size of the Nucleus: Understanding protons, neutrons, and nuclear density.

• Nuclear Force: The forces that hold the nucleus together. 

• Mass-Energy Equivalence (E = mc²): Einstein's equation and its significance in nuclear reactions.

• Nuclear Binding Energy: Understanding nuclear stability and energy release. 

• Radioactivity: Concepts of alpha, beta, and gamma decay. 

• Laws of Radioactive Decay: Half-life, mean life, and decay constant derivations. 

• Nuclear Fission and Fusion: Their role in power generation and astrophysical processes.

• Applications of Nuclear Physics: Uses of radioisotopes in medicine, industry, and archaeology.

Hooke's Law states that within the elastic limit, the stress applied to a material is directly proportional to the strain produced. Mathematically,  

E stands for the modulus of elasticity also called Young's modulus in case of linear deformation.
The Hooke's Law defines the elastic behaviour of materials, determines its elastic limit and helps in material selection for construction and manufacturing. It is used to design springs and elastic components in machines. Hook's law is applicable for the solids within their elastic limit. 
Hooke's law for a spring and other elastic material is shown as:

F is the force applied on the material, k is the spring constant i.e. the stiffness of the material and it depends on the material's geometry and properties, and x is the extension or compression produced.