Question

A wire stretched such that its volume remains constant then poissons ratio is

Answer 1

answer : 0.5

explanation : Poissons ratio is the ratio of longitudinal strain to transverse strain.

Let radius of wire is r and length is l

then, volume of wire, V = πr²l

now differentiating both sides

dV = 2πrl.dr + πr²dl

a/c to question,

volume remains constant

so, dV= 0 = 2πrl.dr + πr²dl

or, 2ldr + rdl = 0

or, 2ldr = -rdl

or, dr/r = -1/2 dl/l

or, longitudinal strain = 1/2 × transverse strain [ we excluded sign ]

or, possions ratio = longitudinal strain/transverse strain

= 1/2 = 0.5