Q.Define Poisson's ratio.

When a wire is stretched, it does not just get longer -- it also gets thinner: its length increases (longitudinal strain) while its diameter simultaneously decreases (lateral strain), exactly the way a stretched rubber band visibly thins as it elongates. POISSON'S RATIO $\mu$, named for the French physicist S. D. Poisson, quantifies this coupled effect as the ratio of the relative contraction (lateral strain) to the relative expansion (longitudinal strain): for a wire of length L and diameter D, with an increase in length l and a decrease in diameter d, $\mu=-\dfrac{d/D}{l/L}=-\dfrac{Ld}{lD}$. The minus sign is a bookkeeping convention flagging that the two strains -- longitudinal (elongation) and lateral (contraction) -- happen in OPPOSITE senses; the ratio itself, being of two dimensionless strains, has NO unit and NO dimension. Poisson's ratio varies widely across materials: it is close to 0.5 for rubber (nearly incompressible -- it contracts sideways almost exactly as much as it stretches lengthwise), around 0.3 for steel, and essentially 0 for cork (cork barely narrows at all when compressed lengthwise, which is exactly why cork is the traditional stopper material for wine bottles -- squeezing it into a bottle neck does not make it bulge and jam). Poisson's ratio is not an independent quantity; it is directly related to the other two elastic moduli through $Y=2\eta_R(1+\mu)=3K(1-2\mu)$, where Y is Young's modulus, $\eta_R$ is the rigidity modulus, and K is the bulk modulus. This relation is the tool used whenever a problem gives the ratio of two elastic moduli (for instance, rigidity modulus as a fraction of Young's modulus) and asks for the material's Poisson's ratio, or vice versa: solving $Y=2\eta_R(1+\mu)$ for $\mu$ gives $\mu=\dfrac{Y}{2\eta_R}-1$.