Question

Poisson’s ratio is defined as the ratio of:
A. Longitudinal stress and longitudinal strain
B. Longitudinal stress and lateral stress
C. Lateral stress and longitudinal stress
D. Lateral stress and lateral strain

Answer 1

Hint: Poisson’s ratio is defined as the ‘fractional change in the transverse length is proportional to the fractional change in the longitudinal length. The constant proportionality is called Poisson’s ratio’. Thus Poisson’s ratio is $\sigma =-{\displaystyle \frac{\mathrm{\Delta }d/d}{\mathrm{\Delta }L/L}}$.

Complete step by step answer:
Stress: If we consider a body with many forces acting on it but its center of mass remains at rest, then due to these acting forces, the body gets deformed and internal forces appear. This is of two types that are longitudinal and shearing stress.

Strain: If we consider a rod of length l being pulled by equal and opposite forces. The length of the rod increases from its natural length $Lto\mathrm{\Delta }L$ . The fraction of ${\displaystyle \frac{\mathrm{\Delta }L}{L}}$ is called longitudinal strain. Shearing strain is produced when a shearing stress is present over the section.

Poisson’s ratio is defined as the ‘fractional change in the transverse length is proportional to the fractional change in the longitudinal length. The constant proportionality is called Poisson’s ratio’. Thus Poisson’s ratio is $\sigma =-{\displaystyle \frac{\mathrm{\Delta }d/d}{\mathrm{\Delta }L/L}}$.
Therefore, Poisson’s ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of the stretching force. Also the ratio of transverse stress to longitudinal stress.

Hence, the correct option is (C).

Note: The longitudinal stress has further two types: compressive stress and tensile stress. And if the length increases from natural length then the longitudinal strain is called the tensile strain and if length decreases it is called compressive strain.If the deformation is small, the stress in a body is proportional to the corresponding strain. ${\displaystyle \frac{\text{Tensile stress}}{\text{Tensile strain}}}=Y$ is a constant.