Question

What is the ratio of lateral strain to a longitudinal strain called?

Answer 1

Hint:The lateral strain is the ratio of change in the diameter of the wire to its change in diameter in longitudinal direction. The longitudinal strain is the ratio of change in the length of the wire to the original length of the wire. This ratio is formulated by Simeon Poisson.

Complete answer:
To answer this question, let’s discuss the meaning of lateral strain and longitudinal strain. The lateral strain is the ratio of change in the diameter of the wire to its change in diameter in longitudinal direction. The longitudinal strain is the ratio of change in the length of the wire to the original length of the wire.

The ratio of lateral strain to the longitudinal strain is called Poisson's ratio. The lateral strain is always negative since the diameter decreases with the applied force. Therefore, we can state Poisson’s ratio as the negative ratio of lateral strain to the longitudinal strain. We denote the Poisson ratio by the letter $$\nu$$. Poisson’s ratio always lies between $$-1$$ and $$+0.5$$. We know that the physical quantity which is the ratio of two similar quantities does not have units. Therefore, Poisson’s ratio is unit less quantity.

According to Poisson’s effect, when we apply the stress in the longitudinal direction of the wire, the length of the wire increases and it’s diameter decreases. We can express Poisson’s ratio as,
$$\nu =-{\displaystyle \frac{{\epsilon }_t}{{\epsilon }_l}}$$
Here, $${\epsilon }_t$$ is the lateral strain or transverse strain and $${\epsilon }_l$$ is the longitudinal strain.

Note:Remember, the negative Poisson’s ratio suggests that the material has undergone the positive strain in the transverse direction even for the positive longitudinal strain. For most of the material, Poisson’s ratio lies between 0 and 0.5. The Poisson’s ratio is unit less and also it is scalar quantity.