Table of Contents

## Introduction:

The elasticity of a material is tied to its bulk modulus. It’s one of the ways to assess a solid’s mechanical properties. Young’s modulus and Shear’s modulus are two other elastic moduli. The bulk elastic characteristics of a material are utilized in all circumstances to determine how much it will compress when subjected to a certain amount of external pressure. Knowing the ratio of the change in pressure to the fractional volumetric compression is crucial. The Bulk Modulus is defined as the change in volume of a body caused by a unit compressive or tensile stress operating uniformly throughout the surface.

**A brief outline:**

- When a substance is equally crushed, its bulk modulus specifies how it reacts. External forces are distributed uniformly throughout the surface of the object when they are perpendicular to the surface. This can also happen when an object is submerged in a liquid and undergoes a volume shift without changing shape.
- P stands for volume stress, which is defined as the ratio of the magnitude of the change in force F to the surface area. The compressibility of a liquid is measured by its bulk modulus. We calculated it as the amount of pressure required to change its volume by one unit.
- The bulk modulus is measured in Pa or KPa units, with MPa being the greater value.
- It is symbolized by the letter K. The force per unit area is its dimension. It’s measured in newtons per square metre (N/m
^{2}) in the metric system.

**Important concepts:**

**The elasticity of bulk modulus:**

While the material displacement is within the elastic limit, the bulk modulus is defined as the fraction of volumetric stress that can contribute to the volumetric strain of a specific material. To put it another way, the bulk modulus is a numerical constant that is used to quantify and describe solid or fluid elastic properties when pressure is put to all surfaces.

The bulk modulus of elasticity is among the mechanical properties of solids that may be measured. Young’s modulus and Shear’s modulus are two other elastic moduli. In any event, a material’s bulk elastic characteristics are used to calculate how much it will compress when subjected to a certain amount of external pressure.

The value is represented by the letter K and has a dimension of force per unit area. In the English system, it is measured in pounds per square inch (psi), while in the metric system, it is measured in newtons per square metre (N/m^{2}).

It’s measured as the proportion of pressure applied to the associated relative decrease in material volume.

**It is represented mathematically as follows:**

**B = ∆P /(V/V)**

Where:

Bulk modulus (B)

P: change in the pressure or force applied to the sample per unit area

V: compression causes a change in the volume of the substance.

V: The material’s initial volume in units of in the English system and N/m2 in the metric system.

**The curve of Stress and Strain:**

An experiment can be used to prove the stress-strain relationship for a specific material under tensile tension. A test cylinder or wire is extended by an external force in a conventional tensile property test. The applied external force required to create the strain, as well as the fractional change in length or strain, are recorded. The external force is gradually increased in phases, and the length change is recorded as well. The stress (which is the same magnitude as the applied external force per unit surface area) and the strain generated is represented on a graph. The graph below is a typical metal graph.

The stress-strain curves differ depending on the material. The stress-strain curves help us comprehend how a material deforms as the load is increased. We can see and determine that the curve is linear in the region of points O and A by looking at the graph. Hooke’s law is respected and obeyed in this location. When the imposed external force is withdrawn, the body returns to its original dimensions. The solid-body acts like an elastic body in this region. Moving forward, stress and strain are not directly related in the region between sites A and B. Even so, when the burden is removed, the body tends to revert to its previous dimensions.

The yield point (also known as the elastic limit) on the curve is called the yield point, and the accompanying stress is called the yield strength (y) of the material. Though the load is increased further, the stress will surpass the yield strength, and the strain will increase rapidly, even if the stress is only slightly increased. The curve between points B and D indicates the same thing.

Powder diffraction beneath applied pressure can be used to determine the bulk modulus. It is a fluid attribute that indicates the fluid’s ability to change the volume under pressure. Just the bulk modulus is relevant for a fluid. These three moduli do not contain enough information to describe the behavior of a complex anisotropic solid like wood or paper, hence the entire generalized Hooke’s law must be used. Isothermal compressibility is defined as the inverse of the bulk modulus at a constant temperature. A substance with a high bulk modulus but low compressibility is difficult to compress. Compressibility is high, while bulk modulus is low, in a substance that is simple to compress. Depending on how heat energy is permitted to travel during the experiment, a bulk modulus measurement can be performed in one of two ways: When a material is pressed and no heat is allowed to flow in or out of the system, it behaves adiabatically (also known as isentropically). Isothermally, where heat can flow in and out to keep the system’s temperature constant.

**Significance of Bulk modulus in NEET exam:**

The bulk modulus **NEET** topics are designed to explain and provide the most common questions that will be asked on the exam. These can be described in simple terms with the help of notes from expert academics in the field, which are available on the Infinity Learn online platform. Multiple-choice questions are simple to practice if students have a good understanding of the concepts covered throughout the curriculum.

Bulk modulus is a term that refers to the number of Important NEET questions that help students prepare for multiple-choice questions, which are common in the required test.

Also read: **Young’s Modulus**

**Frequently asked questions:**

**Question 1: How do compressibility and bulk modulus relate to one other?**

**Answer**: We already know that compressibility and bulk modulus were related in physics. These two notions are mostly concerned with the concepts of pressure and volume. Before we learn about the relationship between compressibility and bulk modulus, it’s important to understand what these terms signify.

**Question 2: What does it mean to be compressible?**

**Answer**: Compressibility is the characteristic of being compressed by pressure into a smaller space. The compressibility of fluid is principally the extent of the change in density that a given change in pressure will cause in the fluid. Gases, on the supplementary hand, are vastly squeezable, while most liquids are not.

**Question 3: Bulk Modulus Dimensional Formula?**

**Answer: **The bulk modulus dimensional formula is as follows:

**[M ^{1} L^{-1} T^{-2}] **

Where,

M = mass

T = Time

L = Length