Question

The Dimensional Formula for Youngs Modulus Is

Answer 1

Step 1: Definition and formula of Young's modulus

Young's modulus is the property of the material that tells how easily we can stretch that material.

Formula: $Y=\frac{Stress}{Strain}=\frac{FL}{lA}$

Where $F$ is the force applied

$L$is the original length

$A$ is the area of cross-section

$l$ is the deformation in the length

Step 2: Finding the dimension of Young's modulus

Substitute all the dimensional formulas of $F,L,A,l$ in the formula respectively.

Dimensional formula of Young's modulus,

$$\begin{gathered} Y=\frac{FL}{lA} \\ \Rightarrow Y=\frac{\left[M^1{L}^1{T}^{-2}\right]\left[M^0{L}^1{T}^0\right]}{\left[M^0{L}^1{T}^0\right]\left[M^0{L}^2{T}^0\right]} \\ \Rightarrow Y=M^1{L}^{-1}{T}^{-2} \end{gathered}$$

Dimensional formula of Youngs modulus $Y$ is $M^1{L}^{-1}{T}^{-2}$