Question

Poisson's Ratio of definition

Answer 1

Poisson 's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force.

Answer 2

Poisson's ratio:-

When a deforming force is applied at the free end of a suspended wire of length l and diameter D, then its length increases by ∆l but its diameter decreases by ∆D.

Now two types of strains are produced by a single force:-

(i) Longitudinal strain = ∆l / l

(ii) Lateral strain = −∆ D/ D

∴ Poisson’s Ratio (σ)

= Longitudinal strain / Lateral strain

= (−∆ D / D) / (∆ l / l )

= −l ∆ D / D ∆ l

→The negative sign shows that longitudinal and lateral strains are in opposite sense.

→As Poisson’s ratio is the ratio of two strains, it has no units and dimensions.

→The theoretical value of Poisson’s ratio lies between – 1 and 0.5. Its practical value lies between 0 and 0.5.

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