Dimensional Formula of Modulus of Elasticity

Modulus of Elasticity is the basic feature that is used for the calculations of the response of the deformations when the value of stress is applied to it. The elastic constants are used to measure the deformation produced through a given stress system that is acting on a material. 

Dimensional formula

The base of the dimensional formula of mobility has an appropriate and proportionate relation with proper dimensions. For instance, dimensional force is F = [MLT-2]. 

Elasticity and its behaviour

When stress application stops, the body regains its unique shape and size. Various materials show diverse elastic behaviour. The study of a material’s flexible behaviour is extremely important. Almost every design plan necessitates knowledge of a material’s flexible conductivity. 

For example, while building a bridge, the amount of traffic that it can bear should be measured accurately in advance. Similarly, when building a crane to lift loads, it is important to remember that the rope’s extension does not exceed its elastic limit. The elastic behaviour of the material utilised must be considered first to solve the problem of bending under stress.

Elastic behaviour of solids

The atoms or molecules inside a solid body are shifted from their specified points or fixed points (equilibrium positions) when it is deformed, resulting in a shift in interatomic and molecular distances. The interatomic force strives to return the body to its initial position when this force is withdrawn. As a result, the body returns to its former shape.

Thus, the material can get distorted depending on the force applied to it. The force that causes the change in the relocation of these particles is known as the twisting force.

As we know, any force has its inverse and equivalent force, which acts in the opposite direction. After the disfiguring force has been expelled, this force encourages the body to regain its original condition.

Dimensional formula of modulus of elasticity

“Young’s modulus, rigidity modulus and bulk modulus” are considered examples of the modulus of electricity. Young’s modulus can be considered as the modulus of electricity examples when the value of the stress is considered to be equivalent to the value of strain. 

The dimensional representation of Modulus of electricity is [M1 L-1 T-2]. In this representation, M represents mass, L represents length and T represents Time.

Coefficient of Elasticity = Stress × [Strain]-1

Or Elasticity = [M1 L-1 T-2] × [M0 L0 T0]-1 = [M1 L-1 T-2]

Application of dimensional analysis 

In real-life physics, dimensional analysis is a crucial part of the measurement. We use dimensional analysis for three main reasons:

● To ensure that a dimensional equation is consistent

● Determining the relationship between physical quantities in physical phenomena

● To switch from one system to another’s units

● Development of a fluid phenomena equation

● To reduce the number of variables necessary in an equation 

Limitations of the dimensional equation

• The principle of homogeneity of dimensions cannot be used for trigonometric and exponential expressions. The derivation is more complex and complicated.

• The comparing terms or factors are less.

• The correctness of the physical expressions depends only on dimensional equality.

• It is majorly used in the case of dimensional constant. We cannot find the value of the dimensionless constant. 

Conclusion

The elastic energy which is stored in the wire if it is suspended vertically through a weight at its lower end can be considered as modulus of elasticity questions. The stress within a leg can also be measured if the man grows and the linear dimension is about to increase by any specific factor. In this scenario, finding out the stress of the leg can be considered as the modulus of elasticity questions.