Young's Modulus And Elastic Modulus

Young’s Modulus (also referred to as the Elastic Modulus or Tensile Modulus), is a measure of mechanical properties of linear elastic solids like rods, wires and such. There are other numbers which give us a measure of elastic properties of a material, like Bulk modulus and shear modulus, but the value of Young’s Modulus is most commonly used. This is because it gives us information about the tensile elasticity of a material (ability to deform along an axis).

The Young’s Modulus of such a material is given by the ratio of stress and strain, corresponding to the stress of material. The relation is given below.

$E$ = $\frac{\sigma}{\epsilon}$

where,

$E$ is the Young’s Modulus of the material given in $N/m^{2}$
$\sigma$ is the stress applied on the material
$\epsilon$ is the strain corresponding to applied stress in the material

With the value of Young’s modulus for a material, the rigidity of the body can be determined. This is because it tell us about the body’s ability to resist deformation on application of force.

The Young’s Modulus values $(x 10^{9} N/m^{2})$ of different material are given below:

• Steel – 200
• Glass – 65
• Wood – 13
• Plastic (Polystyrene) – 3

Quite obviously we can claim that Steel is a lot more rigid in nature than wood or polystyrene, as in its tendency to experience deformation under applied load is less. Young’s modulus is also used to determine how much a material will deform under a certain applied load.

Another thing to keep in mind is that the lower the value of Young’s Modulus in materials, the more is the deformation experienced by the body and this deformation in case of objects like clay and wood can vary in the one sample itself. One part of the clay sample deforms more than the other whereas a steel bar will experience an equal deformation throughout.

Try calculating the change in length of a steel beam, whose initial length was 200m, due to an applied stress of $1.5 N/m^{2}$. The Young’s modulus of steel can be found in the table above.

Young’s Modulus Important Questions

Q1. What is Young’s modulus?

Ans: Young’s modulus is also known as modulus of elasticity and is defined as the mechanical property of a material to withstand the compression or the elongation with respect to its length. It is denoted as E or Y.

Q2. What is the SI unit of Young’s modulus?

Ans: Pascal is the SI unit of Young’s modulus.

Q3. What is the dimensional formula of Young’s modulus?

Ans: The dimensional formula of Young’s modulus is [ML-1T-2].

Q4. What is the formula of Young’s modulus?

Ans: Young’s modulus is given as:

Y= (F.L)/(A.ΔL)

Where,

• Y is the Young’s modulus
• F is the force applied
• L is the length of the material
• A is the area of the section
• ΔL is the change in the length of the material after the force is applied

Q5. What is strain?

Ans: Strain is defined as the deformation per unit length.

Q6. What is ductility?

Ans: Ductility is defined as the property of a material by which the material is drawn to a smaller section by applying tensile stress.

Q7. Give examples of dimensionless quantities.

Ans: Following are the examples of dimensionless quantities:

• Poison’s ratio
• Strain

Q8. What happens to Young’s modulus with an increase in temperature?

Ans: As the temperature increases, Young’s modulus decreases.

Q9. Give an example of a material with the highest elasticity.

Ans: Steel is an example of a material with the highest elasticity.

Q10. What is the theoretical value of Poisson’s ratio?

Ans: The theoretical value of Poisson’s ratio lies between -1 to 0.5.

Practise This Question

A wire 4 m long and 0.3 mm diameter is stretched by a force of 100N. If the extension in the wire is 0.3 mm, calculate the potential energy stored in the wire.