Dimensional Formula of Young's Modulus of Elasticity

Young's Modulus is a mechanical property that measures the stiffness of a solid material. It tells us how easily a material can bend or stretch. It is a core concept in the study of Elasticity in Class 11 Physics.

Question (Click to Flip)

Which material has a higher Young's Modulus: Rubber or Steel?

Answer

Steel has a vastly higher Young's Modulus than rubber. In physics, steel is considered much more 'elastic' than rubber because it requires much more force to deform it, and it snaps back to its original shape forcefully.

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Key Facts

Because Stress is essentially Force/Area, the dimensional formula of Young's Modulus is identical to the dimensional formula for Pressure.

The SI unit of Young's Modulus is Pascals (Pa) or Newtons per square meter ($N/m^2$).

1. The Base Formula

Young's Modulus ($Y$) is defined as the ratio of tensile stress to tensile strain. Formula: $Y = \frac{\text{Stress}}{\text{Strain}}$

2. Finding the Dimensions of Components

Strain: Strain is defined as the change in length divided by the original length ($\Delta L / L$). Because it is a ratio of two lengths, it has no dimensions. $[M^0 L^0 T^0]$.
Stress: Stress is defined as Force applied per unit Area ($F/A$).
- Dimension of Force = $[M^1 L^1 T^{-2}]$
- Dimension of Area = $[L^2]$
- Dimension of Stress = $\frac{[M^1 L^1 T^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}]$

3. The Final Derivation

Since Strain is dimensionless, the dimensional formula of Young's Modulus is exactly the same as the dimensional formula of Stress.

Final Dimensional Formula = $[M^1 L^{-1} T^{-2}]$

Questions and Answers

Which material has a higher Young's Modulus: Rubber or Steel?+

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