JEE Main & Advanced Physics Elasticity Poisson's Ratio

When a long bar is stretched by a force along its length then its length increases and the radius decreases as shown in the figure.           

Lateral strain : The ratio of change in radius or diameter to the original radius or diameter is called lateral strain.

Longitudinal strain : The ratio of change in length to the original length is called longitudinal strain.           

The ratio of lateral strain to longitudinal strain is called Poisson's ratio \[(\sigma )\].

i.e. \[\sigma =\frac{\text{Lateral strain}}{\text{Longitudinal strain}}\]

\[\sigma =\frac{-dr/r}{dL/L}\]

Negative sign indicates that the radius of the bar decreases when it is stretched. Poisson's ratio is a dimensionless and a unitless quantity.