Question

Select the pair whose dimensions are same.

• A. Pressure and stress
• B. Stress and strain
• C. Pressure and force
• D. Power and force

Answer 1

The correct option is A Pressure and stress

Find the dimension of Pressure and stress.
As we know,
$\text{Pressure =}\frac{\text{Force}}{\text{Area}}\dots \left(i\right)$
Dimension of $F=\left[ML{T}^{-2}\right]$
Dimension of $A=\left[L^2\right]$
By putting the dimensions in equation $\left(i\right)$ we get,
$P=\frac{ML{T}^{-2}}{L^2}=\left[M{L}^{-1}{T}^{-2}\right]$

$\text{Stress =}\frac{\text{Resisting Force}}{\text{Area}}=\frac{F}{A}\dots \left(ii\right)$
By putting the dimensions in equation $\left(ii\right)$ we get,
$\text{Stress}=\frac{ML{T}^{-2}}{L^2}=\left[M{L}^{-1}{T}^{-2}\right]$

Check the similarity of dimension.
Dimension of stress = $\left[M{L}^{-1}{T}^{-2}\right]$
Dimension of pressure = $\left[M{L}^{-1}{T}^{-2}\right]$
This shows that dimensions of stress and pressure is same.