Question

What is the ratio of stress to strain called within the limit of elasticity?

Answer 1

Hint: The stress is the applied force per unit area of cross-section. The strain is the ratio of change in dimensions of the body to the original dimensions of the body. Recall Hooke’s law of elasticity which states that the stress is proportional to the strain within the limit of elasticity. The proportionality factor is what we want to define.

Complete answer:
To answer this question, let’s discuss the meaning of stress and strain. The stress is the applied force per unit area of cross-section. If we apply the force to stretch the rigid rod, the stress is referred to as a uniaxial stress. The strain is the ratio of change in dimensions of the body to the original dimensions of the body. Therefore, the strain is a measure of the amount of deformation produced in the body. If we apply stress on the body to stretch it and after the stress is removed, if the body regains its original length, the body is said to be an elastic body and the property is known as elasticity.

From Hooke’s law, we know that the stress is proportional to the strain produced in the body within the elastic limit. Therefore, we can express Hooke’s law as,
\[{\text{stress}} \propto {\text{strain}}\]
\[ \Rightarrow {\text{stress}} = \left( E \right)\,\left( {{\text{strain}}} \right)\]
\[ \therefore\dfrac{{{\text{stress}}}}{{{\text{strain}}}} = E\]
The proportionality factor E is known as Modulus of elasticity or Young’s modulus of elasticity.

Therefore, we have the Young’s modulus of elasticity is the ratio of the stress to the strain.

Note:Do not get confused between modulus of elasticity and modulus of rigidity. The modulus of rigidity measures how rigid the body is. There is another ratio called Poisson’s ratio, which is the ratio of transverse strain to axial strain and not the ratio of stress to strain.