Dimensional Formula of Stress

Dimensional Formula of Stress is M¹L^-1T^-2

Dimensional Formula is an expression that defines the power of fundamental quantities, i.e. Mass, Length, and Time in units of a quantity. Every physical quantity has its dimensional formula. Other fundamental quantities such as electric current (A) and thermodynamic temperature (K) are also used in the dimensional formula of some quantities.

In this article, we will learn about the dimensional formula of stress and how to derive it.

What is Stress?

Stress in physics and engineering is the restoring force induced per unit area in a body due to externally applied forces. According to Newton’s 3rd law, the restoring force induced is equal and opposite to the applied force, therefore, sometimes stress is referred to as force exerted per unit area of an object or a body. However, force exerted per unit area of a body is termed as pressure. Thus, stress and pressure may be the same in magnitude but they have different meanings.

Stress Definition

Stress is a physical quantity that is used for the restoring force developed in a body in response to an applied force per unit area.

Formula for Stress

Mathematically, stress is defined as,

Stress = Force/Area

where,

• Force = Restoring Force developed in the body.
• Area = Area over which the force is applied on the body

Stress is represented by the Greek Symbol σ. It finds significance in various concepts of physics and engineering applications.

Dimensional Formula of Stress

Dimensionally Stress is defined as [M ¹L ^-1T ^-2]

Derivation of Dimensional Formula of Stress

Let us see that how the above mentioned dimensional formula has been obtained. As, we know that, mathematically, stress is force per unit area. So, we write it as follows.

Stress = Force/Area

Now, Force = Mass X Acceleration, so dimensional formula of force comes out to be [M¹ L¹ T^-2]. And, dimensional formula of Area is [M⁰ L² T⁰]. Hence,

Dimensional Formula of Stress = [M¹ L¹ T^-2] / [M⁰ L² T⁰] = [M¹ L^-1 T^-2]

Thus, we derive the dimensional formula of stress as [M L^-1 T^-2].

Advantages of Dimensional Formula

The dimensional formula of a physical quantity tells us about its units in terms of fundamental quantities. Below are some advantages of the dimensional formula.

• It can be used to check the dimensional consistency of a physical equation.
• It is used to derive empirical formula of quantities depending on other physical quantities.
• It is used for conversion from one system of units to the other.
• It is also used to determine units of constants involved in a physical equation.

Limitations of Dimensional Formula

Although dimensional formula is an useful expression but it has some limitations listed as follows:

• Dimensional formula can help us find out the empirical formula but it does not give any information about value of any constants involved in the actual formula.
• Dimensional formula alone can’t be used to check correctness of any physical equation.

Conclusion

Stress is defined as force per unit area, symbolized as F/A. Consequently, the dimensional formula for stress is [ML^-1T^-2], and its units are Pascals (Pa) or N/m².

Read More,

• Stress in Physics
• Stress Formula
• Stress and Strain
• Dimensional Formulas

Dimensional Formula of Stress: FAQs

1. What is Stress, its Unit and Dimension?

Stress is a physical quantity that represents the internal forces that neighboring particles of a continuous material exert on each other. SI unit of stress is Pascal (Pa) and its dimension is [ML^-1T^-2].

2. What is the Formula for Stress?

Stress (σ) is calculated as σ = F/A, where F is the force applied perpendicular to the surface of an object and A is the area over which the force is distributed.

3. What is the Dimension of Stress?

Dimension of Stress is [ML^-1T^-2].

4. What Physical Quantity has Same Dimension as Stress?

Pressure has the same dimensional formula as stress i.e., [ML^-1T^-2].

5. What is Dimensional Formula for Thermal Stress?

The dimensional formula for thermal stress is the same as that for stress, [ML^-1T^-2], since thermal stress is a type of stress.

6. What is the Dimensional Formula of Tension?

As a force, the dimensional formula for tension is [ML¹T^-2].