What is Poisson’s Ratio?

SOLUTION

CONCEPT:

• When a long bar is stretched by a force along its length than its length increases and the radius decreases.

• 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.

EXPLANATION:

• Poisson's ratio: The ratio of lateral strain to longitudinal strain is called Poisson’s ratio (σ). Therefore option 1 is correct.

\(\sigma = \frac{{{\rm{Lateral\;strain}}}}{{{\rm{Longitudinal\;strain}}}}\)

\(\sigma = \frac{{ - \frac{{dr}}{r}}}{{\frac{{dL}}{L}}} = - \frac{{dr \times L}}{{dL \times r}}\)

• The negative sign indicates that the radius of the bar decreases when it is stretched.
• Poisson’s ratio is a dimensionless and a unitless quantity.
• The ratio of force to the area is pressure. Therefore option 2 is incorrect.
• The ratio of change in radius or diameter to the original radius or diameter is called lateral strain. Therefore option 3 is incorrect.
• The ratio of change in length to the original length is called longitudinal strain. Therefore option 4 is incorrect.