Collegedunia Team Content Curator
Content Curator
Young’s Modulus can be defined as the measurement of a material’s ability to defy changes in length during lengthwise tension or compression. It is also referred to as the modulus of elasticity. Young’s modulus is equivalent to the longitudinal stress divided by the strain. Modulus of elasticity can be defined as the measure of the stress-strain relationship of the object.
It is one of the important features within the calculation of the deformation response of concrete, once the stress is applied. Elastic constants are those constants that verify the deformation made by a given stress system performing on the material. The formula of Young’s modulus = stress/strain = \(E = \frac{\sigma}{\epsilon}\).
Elastic constants help determine the deformation which is generated by a given stress system on a material. Some of the types of elastic constants are:
- Young’s modulus or modulus of Elasticity (E)
- Bulk modulus (K)
- Poisson’s Ratio (µ)
- Shear modulus or modulus of rigidity (G)
| Table of Content |
Key Terms: Young’s Modulus, Stress, Strain, Longitudinal Stress, Modulus of Elasticity, Deformation, Compression, Tensile Modulus
What is Young’s Modulus?
[Click Here for Sample Questions]
Young’s modulus is referred to as the modulus of elasticity and can be defined as any material consisting of a mechanical attribute that helps it to withstand the elongation or compression of its length. It is denoted as E or Y.
Young’s Modulus (also called Elastic Modulus or Tensile Modulus), is a measure of the mechanical properties of linear elastic solids like rods, wires, and more. Young’s modulus represents the relationship stress, i.e., force per unit area and strain, i.e., proportional deformation in an object share.
Young’s Modulus
Some other numbers, like Bulk Modulus and Shear Modulus, also help measure the elastic properties of a material. However, Young’s Modulus is still one of the most commonly used. Young’s Modulus is most commonly used because it provides information about the tensile elasticity of a material, i.e., the capacity to deform along an axis.
A solid object deforms after a specific load is applied to it. If the object is made of elastic, it regains its original form when the pressure is removed. Several materials are not linear and elastic beyond a little amount of deformation. The constant Young’s modulus applies solely to linear elastic substances.
Read More:
| Topic Related Links | ||
|---|---|---|
| Elastic Limit | Stress | Bulk Modulus |
| Hooke's Law | Derivation Relation between Elastic Constants | Shear Modulus |
Formula of Young’s Modulus
[Click Here for Previous Years Questions]
The formula of Young’s Modulus is:
| \(E = \frac{\sigma}{\epsilon}\) |
Young’s Modulus Formula From Other Quantities:
| \(E\equiv \frac{\sigma (\epsilon )}{\epsilon }=\frac{\frac{F}{A}}{\frac{\Delta L}{L_{0}}}=\frac{FL_{0}}{A\Delta L}\) |
Here,
- E is Young’s modulus in Pa
- σ is the uniaxial stress in Pa
- ε is the strain or proportional deformation
- F is referred to as the force exerted by an object under tension
- A is the actual cross-sectional area
- ΔL is the change in the length
- L0 is the actual length
Units and Dimensions of Young’s Modulus
Some important facts to note about Young’ Modulus are:
| Parameters | Units and Dimensions |
|---|---|
| SI unit | Pa |
| Imperial Unit | PSI |
| Dimension | ML-1T-2 |
Young’s Modulus of such a material is given by the ratio of stress and strain, such as the stress of the material. The relation is given below.
⇒ E = σ/∈
Where,
- E is the Young’s Modulus of the material given in N/m2
- σ is the stress applied to the material
- ∈ is that the strain comparable to applied stress within the material
With the value of Young’s modulus for a material, the rigidity of the body is determined. This is often as a result of the body’s ability to resist deformation on the application of force.
The Young’s Modulus values (x109N/m2) of various materials are given below:
| Materials | Values |
|---|---|
| Steel | 200 |
| Glass | 65 |
| Wood | 13 |
| Plastic (Polystyrene) | 3 |
These are some of the important values associated with different materials.
Read More:
Young’s Modulus Factors
[Click Here for Sample Questions]
Young’s modulus is used to verify what proportion a material can deform underneath an applied load.
- By understanding the modulus of elasticity of steel, it can be said that steel is more rigid than wood or polystyrene. This is because its tendency to undergo deformation underneath the applied load is a smaller amount.
- Lower the value of Young’s Modulus in materials, the more the body will undergo deformation. Typically, the deformation in case of clay or wood can differ in one particular sample itself.
- In case of a clay sample, one part deforms more than the other, while in a steel bar, the deformation takes place equally throughout.
According to varied experimental observations and results, the magnitude of the strain created in a given material is the same, irrespective of whether or not the strain is tensile or compressive. Young's modulus denoted by the symbol 'Y' is outlined or expressed because of the ratio of tensile or compressive stress (σ) to the longitudinal strain (ε).
⇒ Y = σ ε
We have,
A strain could be a dimensionless quantity, the unit of Young’s modulus is the same as that of stress, that's N/m2 or Pascal (Pa).
Examples of Young’s ModulusQues. Determine Young’s modulus, when two N/m² stress is applied to provide a strain of 0.5. [2 marks] Ans. As per the given question, σ = 2 N/m² Strain, ε = 0.5 Young’s modulus formula can be expressed by, E = σ / ∈ = 2 / 0.5 = 4 N/m² Ques. Determine Young’s modulus of a material whose elastic stress and strain are four N/m2 and zero.15 respectively? [2 marks] Solution: As per the given question, Stress, σ = 4 N/m² Strain, ε = 0.15 Young’s modulus formula is expressed by, E = σ / ∈ E = 4 / 0.15 = 26.66 N/m² |
Previous Year Questions
- A load of 1 kg weight is attached to one end of a steel wire of area … [BITSAT 2008]
- There is some change … [BITSAT 2008]
- If the ratio of lengths, radii and Young's modulus of steel … [VITEEE 2009]
- One end of a horizontal thick copper wire of length … [JEE Advanced 2013]
- A copper wire of length 2.2m and a steel wire … [KCET 2013]
- A light rod of length 100 cm is suspended from the ceiling horizontally … [AP EAPCET]
- A copper wire and a steel wire of the same diameter and length … [BHU UET]
- A steel wire can withstand a load up to … [BITSAT 2008]
- When a rod is heated but prevented from expanding the stress … [BHU UET]
- Two wires A and B are stretched by the same load … [KCET 2018]
- Four wires of the same material are stretched by the same load …
- Two wires of same length and same material … [KEAM]
- The breaking stress of a wire of length ll and radius r is …
- Two wires are made of the same material and have the same volume … [NEET 2018]
- When a block of mass … [NEET 2019]
Things to Remember
- Young’s Modulus is the measurement of a material's ability to defy length changes during lengthwise tension or compression.
- Young’s Modulus is also referred to as the modulus of elasticity.
- The formula of Young’s Modulus is \(E = \frac{\sigma}{\epsilon}\).
- Dimension of Young’s Modulus is ML-1T-2.
Important Handwritten notes of Mechanical Properties of Solids:
Sample Questions
Ques. Give samples of dimensionless quantities. (2 marks)
Ans. Following are the instances of dimensionless quantities:
- Poisson's ratio
- Strain
Ques. Give an example of a material with the highest elasticity. (1 mark)
Ans. Steel is an example of a material with the highest elasticity.
Ques. What is ductility? (1 mark)
Ans. Ductility is defined because of the property of a material by which the material is drawn to a smaller section by applying tensile stress.
Ques. What is the dimensional formula of Young’s modulus? (1 mark)
Ans. The dimensional formula of Young’s modulus is [ML-1T-2].
Ques. What is the SI unit of Young’s modulus? (1 mark)
Ans. Pascal is the SI unit of Young’s modulus.
Ques. What is Young’s Modulus? (1 mark)
Ans. Young’s modulus can be expressed as the modulus of elasticity of materials consisting of a mechanical attribute that helps it to withstand the elongation or compression of its length.
Ques. Define modulus of rigidity. (1 mark)
Ans. The modulus of rigidity can be expressed as the ratio of shear stress in relation to shear strain in a body.
Ques. What is the unit of shear strain? (1 mark)
Ans. Shear strain is typically a dimensionless physical quantity. Thus, it has no unit.
Ques. A cord with original length of 100 cm has been pulled by force, causing a change in length of 2 mm. Thus, find out its strain. (2 marks)
Ans. As per the given question, it can be said:
Original length (l0) = 100 cm = 1 m
Change in length (Δl) = 2 mm = 0.002 m
Thus, Strain = \(\frac{change \ in \ length (\Delta l) }{original \ length \ (l_0)}\)
Strain = \(\frac{0.002 \ m}{1 \ m}\)
= 0.002 m
Ques. A string of 4 mm in diameter has an original length of almost 2 m. Once it is pulled by a force of 200 N, the final length becomes 2.02 m, determine. If the stress and strain are 15.92 x 106 N/m2 and 0.01 respectively, determine Young’s modulus. (3 marks)
Ans. As per the given question,
Diameter (d) = 4 mm = 0.004 m
Radius (r) = 2 mm = 0.002 m
Area (A) = π r2 = (3.14)(0.002 m)2
Area (A) = 0.00001256 m2 = 12.56 x 10-6 m2
Force (F) = 200 N
And, Original length of spring (l0) = 2 m
Change in length (Δl) = 2.02 – 2
= 0.02 m
Young’s Modulus = \(\frac{Stress}{Strain}\)
= \(\frac{15.92 \times 10^6 N/m^2}{0.01}\)
= 1592 x 106 N/m2
= 1.6 x 106 N/m2
Read Also:
Comments