Young’s modulus, a fundamental property in material science, quantifies the stiffness of a material. It describes the relationship between stress (force per unit area) and strain (relative deformation) in elastic materials. Understanding the dimensions of Young's modulus is crucial for engineering, physics, and material studies.
Young’s modulus measures how a material resists deformation under tensile or compressive forces. It is denoted by the symbol E and is calculated using the formula:
E = Stress / Strain
This equation shows that Young's modulus dimensional formula is derived from the dimensions of stress and strain.
Also Check: Important Topic of Physics: Elastic Behaviour
The dimensional formula of Young Modulus is given by,
[M1 L-1 T-2]
Where,
Young’s Modulus (Y) = Linear Stress × [Linear Strain]-1. . . . . (1)
Since, linear stress = Force × Area-1 . . . . . . (2)
Force = M × a = M × [M0 L1 T-2] . . . . (3)
Area = m2 = [M0 L2 T0] . . . . (4)
From equation (2), (3), and (4) we get,
The dimensional formula of linear stress = [M1 L-1 T-2] . . . . (5)
And, linear strain = Change in length × [Original length]-1 = Dimension Less
On substituting equation (5) in equation (1) we get,
Young’s Modulus = Linear Stress × [Linear Strain]-1
Or, Y = [M1 L-1 T-2]
Therefore, momentum is dimensionally represented as [M1 L-1 T-2].
Also Check: Kinetic Work Energy Theorem
The SI unit of Young’s modulus is Pascals (Pa), which is equivalent to:
1 Pa = 1 Nm-2
This indicates that Young's modulus in Pascals is a direct representation of the force applied per unit area.
When studying materials, it’s important to understand Young's modulus units and dimensions in various systems. While Pascals (Pa) is the SI unit, it is often converted to other units like:
Using tools like a Young's modulus unit conversion calculator can simplify these conversions.
The measurement units of Young's modulus depend on experimental setups that calculate stress and strain under applied loads. Accurate methods ensure precise material characterization, helping engineers select the right materials for construction, aerospace, and manufacturing.
Young's modulus is a measure of the stiffness of a material. It quantifies the relationship between stress (force per unit area) and strain (proportional deformation) in a material within the elastic limit.
SI Unit: The SI unit of Young's modulus is Pascal (Pa), which is equivalent to N/m² or kg·m⁻¹·s⁻².
Dimension: The dimensional formula of Young's modulus is [M L⁻¹ T⁻²].
The formula for Young's modulus Y is:
Y = Stress / Strain
Stress = Force / Area (F/A)
Strain = Change in length / Original length (ΔL/L)
Substituting the values: Y = (F/A) / (ΔL/L) = (F · L) / (A · ΔL)
The dimensional formula of any modulus of elasticity (including Young's modulus) is the same as that of pressure or stress. It is [M L⁻¹ T⁻²].
The dimension of Young's modulus is [M L⁻¹ T⁻²], where:
M represents mass,
L represents length,
T represents time.
The dimension of Young's modulus Y is [M L⁻¹ T⁻²], as it relates stress (force per unit area) to strain (dimensionless).