Explain Poisson's Ratio.

Explanation

Observation from Young.s modulus indicates that when the weight is suspended below the wire its cross sectional radius slight decreases.
If tensile force is applied to body its length increases but magnitude of lateral dimensions perpendicular to the length decreases.Here wire is taken so diameter decreases.
If compressed force applied, its length decreases and hence its diameter means lateral dimension increases.
Simon Poisson find out that lateral strain is directly proportional to the longitudinal strain.
The ratio of lateral strain and longitudinal strain is known as Poisson ratio.
`therefore` Poission.s Ratio` = ("lateral strain")/("longitudinal strain")`
If original diameter of wire is d and change in diameter due to stress in `Delta d` then lateral strain is `(Delta d)/(d).`
If original length of wire is L and change in length due to stress is `Delta L` then longitudinal strain is `(DeltaL)/(L).`
Hence, Poisson ratio `(mu)` is the ratio of lateral strain and longitudinal strain.
`therefore mu = (((Delta d )/( d )))/(((Delta L)/( L )))or ((Delta d )/( Delta L)) xx ((L)/(d ))`
Since Possion ratio is the ratio of two strains. So it has no unit and dimension.
Its value depends on the type of material.
Its vlaue for steel is between `0.28` to `0.30.` Its value for aloys of aluminium is almost `0.33.`