Dimensions Of Young’s Modulus

When we stretch an elastic band, the length of the band increases, and it might break after some time due to the pressure. When we apply pressure on a certain object, the size and shape of the object changes. These changes occur due to stress and strain. How would you calculate the stress and strain on the objects? Young’s modulus shows the relation between stress and strain of any material.

Table of Contents

What is Young’s modulus?
Dimensional formula of Young modulus
Practice problems
FAQs

What is Young’s Modulus?

Young's modulus, commonly known as the Elastic modulus or Tensile modulus, is an indicator of the structural characteristics of solids that are linearly elastic. Young's modulus illustrates the relation between strain (proportional deformations in an object) and stress (force per unit area).

When a certain load gets applied to a solid object, it deforms. Once the load is released, an elastic object returns to its original shape. Several materials are not linear and elastic after a certain degree of deformation. Young's modulus is a constant that only applies to linearly elastic materials.

The stress-strain ratio determines Young's modulus found in such an object. The degree of rigidity of an object can be determined by calculating using the value of Young's modulus for a substance.

Young's modulus can also be described as a material's structural ability to tolerate compression or extension when compared to its original dimension. It is denoted by the letters E or Y.

The SI unit of Young’s modulus is Pascal (Pa) or N/m². Young’s Modulus is given by the formula:

formula

Dimensional Formula of Young’s Modulus

Physical quantities are defined using their dimensions, which express the fundamental characteristics of the quantity and the unit of measurement. Basic foundation units are commonly used to express dimensions. Every physical quantity has a distinct set of dimensions that demonstrate its essential properties and how it is measured.

Young's modulus is an object characteristic related to how rigid a solid material is. It measures the ratio of strain to stress in a material that is being compressed or under tension. Young's modulus can be described by the ratio of the longitudinal stress to the longitudinal strain under the elastic limit.

The dimensional formula of Young’s modulus is given by

[M¹L^-1T^-2]

Where ll

M = mass

L = length

T = time

We can derive the dimensional formula for Young’s modulus.

Derivation of the Dimensional Formula of Young’s Modulus

formula

Dimension for the area is given as

formula

Practice Problems

Q1. Young’s modulus is usually measured by?

a. The difference between stress and strain
b. The product of stress and strain
c. The ratio of stress to strain
d. The sum of stress and strain

Ans. c. The ratio between the stress and strain of a material is defined as Young’s modulus of material.

Q2. What is the unit of Young’s modulus?

a. Joules
b. Pascals
c. Unitless
d. Newtons

Ans. b. The SI unit of Young’s modulus is Pascal or N/m2.

Q3. What is the dimensional formula of Young’s modulus?

formula

FAQs

Q1. What physical quantity has the same dimensions as Young’s modulus?
Ans. Strain is a dimensionless physical quantity. Stress has the same dimension as Young’s modulus.

Q2. What is the unit of shear strain?
Ans. The shear strain of a material is measured in radians and therefore has no units.

Q3. What is Hooke’s law of elasticity?
Ans. Hooke’s law of elasticity states that the amount of force needed to stretch an elastic object, such as a metal spring, is directly proportional to a spring's extension under specific limits.