Question

Dimension formula of stress is the same as that of.

Answer 1

Hint: Stress is a physical term that describes the force exerted to a substance per unit area. The object deforms when the deforming force is given to it. An opposing force will be generated inside the item in order to restore the thing to its previous shape and size which is called stress.

Formula used:
$\sigma = \dfrac{F}{A}$
Where,
     $F = $Restoring force measured in Newton.
     $A = $Area of cross-section in ${m^2}$ .
     $\sigma = $Stress Measured in $N/{m^2}$ .

 Complete step by step solution:
The applied deforming force will be equivalent in magnitude and direction to the restoring force. Stress is the measurement of the restoring force created per unit area of the material.
The stress is directed in the opposite direction as the external force. Stress has a structural quality to it. It arose within a person's body in response to an external influence. Inside the solid, the stress might vary in different directions.
As a result, stress is defined as the material's restoring force per unit area. So, it's a tensor quantity. The Greek letter $\sigma $ is used to represent it. Pascal or $N/{m^2}$ are the units of measurement. Mathematically,
     $\sigma = \dfrac{F}{A}$
Dimension of Force $ = [ML{T^{ - 2}}]$
Dimension of Area $ = [{M^0}{L^2}{T^0}]$
Therefore, Dimension of Stress $ = [ML{T^{ - 2}}]/[{M^0}{L^2}{T^0}]$
                    $ = [M{L^{ - 1}}{T^{ - 2}}]$
Dimension of pressure $ = [M{L^{ - 1}}{T^{ - 2}}]$
The above dimension of the quantity, stress is equal to that of pressure. So the dimension formula of stress is equal to that of pressure.

Note: Stress and pressure are two words that are frequently interchanged. Pressure is defined as the amount of force applied per unit area. Stress, on the other hand, is the amount of force exerted per unit area that a material experiences.