Question

The dimensional formula for Young’s modulus is

• A. $ML^{-1}T^{-2}$
• B. $M^{0}LT^{-2}$
• C. $MLT^{-2}$
• D. $ML^{2}T^{-2}$

Answer 1

Answer: (A)

Young’s modulus $=\frac{\text{Stress}}{\text{Strain}}$
Strees $=\frac{\text{Force}}{\text{Area}}\Rightarrow \left[\sigma\right]=\frac{\left[MLT^{-2}\right]}{\left[L^{2}\right]}$
$=\left[ML^{-1}T^{-2}\right]$
Strain $=\frac{\text{Chinge in length}}{\text{Original length}}$
Hence strain is dimensionless
Hence $\left[Y\right]=\left[ML^{-1}T^{-2}\right]$