Question

The dimensional formula for the bulk modulus of elasticity is _______.

Answer 1

1. Bulk modulus of elasticity: It is defined as the ratio of volumetric stress to the volumetric strain of a specific material, while the material deformation is within the elastic limit.
2. It is denoted by the symbol K.
3. Mathematically, it is written as: $K=\frac{VolumetricStress}{VolumetricStrain}$
4. Calculation for the dimensional formula for the bulk modulus of elasticity:
   $K=\frac{VolumetricStress}{VolumetricStrain}=\frac{P}{{\displaystyle \raisebox{1ex}{$∆V$}\!\left/ \!\raisebox{-1ex}{$V$}\right.}}$
   The dimensional formula of P is $\left[M{L}^{-1}{T}^{-2}\right]$.
   $$\begin{gathered} \Rightarrow \left[K\right]=\frac{\left[M{L}^{-1}{T}^{-2}\right]}{{\displaystyle \raisebox{1ex}{$\left[L^3\right]$}\!\left/ \!\raisebox{-1ex}{$\left[L^3\right]$}\right.}} \\ \Rightarrow \left[K\right]=\left[M{L}^{-1}{T}^{-2}\right] \end{gathered}$$

Thus, the dimensional formula for the bulk modulus of elasticity is $\left[M{L}^{-1}{T}^{-2}\right]$.