Young’s Modulus Formula

Introduction

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.

Young’s Modulus Formula

\(E=\frac{\sigma }{\epsilon }\)

Young’s Modulus Formula From Other Quantities

\(E\equiv \frac{\sigma (\epsilon )}{\epsilon }=\frac{\frac{F}{A}}{\frac{\Delta L}{L_{0}}}=\frac{FL_{0}}{A\Delta L}\)

Notations Used In The Young’s Modulus Formula

  • E is Young’s modulus in Pa
  • 𝞂 is the uniaxial stress in Pa
  • ε is the strain or proportional deformation
  • F is the force exerted by the object under tension
  • A is the actual cross-sectional area
  • ΔL is the change in the length
  • L0 is the actual length

Young’s Modulus Units And Dimension

SI unit Pa
Imperial unit psi
Dimension ML-1T-2

Solved Examples

Example 1Determine 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 2Determine 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

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Practise This Question

The mode of the data set given below is 13. Find the missing observation.

5          ?          6          34        13        5          9          13        9         19        45