# Hooke’s Law | Modulus of Elasticity

## Stress & Strain | Mechanical Properties of Solids-

Before you go through this article, make sure that you have gone through the previous articles on Stress and Strain.

We have learnt-

• When a deforming force is applied on a body, a restoring force is produced in it.
• This restoring force per unit area of the body is called as stress.
• The effect of stress is to produce distortion or change the configuration of the body.
• The ratio of the change in configuration to the original configuration is called as strain.
• Strain measures the degree of deformation.

## Hooke’s Law-

In mechanical properties of solids, Hooke’s law is defined as-

 For sufficiently small stresses, stress is directly proportional to the strain.

#### Mathematically,

Here, this constant is called Modulus of Elasticity or Elastic Modulus. Thus,

### Characteristics of Modulus of Elasticity-

• Its SI unit is same as that of stress i.e. newton per square meter (Nm-2) or pascal (Pa).
• Its dimensional formula is same as that of stress i.e. [ML-1T-2].
• It is a scalar quantity.
• Its value depends on the nature of material of the body and is independent of its dimensions.
• It is a measure of rigidity or stiffness of a material. Greater the modulus, the stiffer the material.

## Types of Modulus of Elasticity-

Since strain is of three types, therefore modulus of elasticity is also of three types-

Let us discuss all types of modulus of elasticity one by one in detail.

### 1. Young’s Modulus of Elasticity-

It is defined as the ratio of the longitudinal stress on the material to the longitudinal strain produced in the material.

### 2. Bulk Modulus of Elasticity-

It is defined as the ratio of the bulk stress (or volume stress) on the material to the volume strain produced in the material.

### 3. Shear Modulus or Modulus of Rigidity-

It is defined as the ratio of the tangential stress (or shearing stress) on the material to the shear strain produced in the material.