# Youngs Modulus Formula

Young’s modulus which can also be called as elastic modulus is a mechanical property of linear elastic solid substances. It describes the relationship between stress (force per unit area) and strain (proportional deformation in an object. The Young’s modulus is named after the British scientist Thomas Young.

A solid object deforms when a particular load is applied to it. If the object is elastic, the body regains its original shape when the pressure is removed. Many materials are not linear and elastic beyond a small amount of deformation. The constant Young’s modulus applies only to linear elastic substances.

The Young’s modulus formula is given by,

$E\,&space;=\,&space;\frac{\sigma}{\epsilon&space;}$

Where,

E = Young’s modulus

s = stress

e = strain

Example 1

Determine the Young’s modulus, when 2N/m2 stress is applied to produce a strain of 0.5.

Solution:

Given:

Stress, σ = 2 N/m2

Strain, ε = 0.5

Young’s modulus formula is given by,

E = σ / ϵ

= 2 / 0.5

=4 N/m2

Example 2

Determine the Young’s modulus of a material whose elastic stress and strain are 4 N/m2 and 0.15 respectively?

Solution:

Given:

Stress, σ = 4 N/m2

Strain, ε = 0.15

Young’s modulus formula is given by,

E = σ / ϵ

E = 4 / 0.15

=26.66 N/m2