Question

the volume of a wire remains unchanged when the wire is sunbjected to a tension. Find the poissons ratio of the material of the wire

Answer 1

Volume = Area x Length

a l = (a - Δa ) (l + Δl)

a = πr²

Δa = 2πrΔr

πr²l = (πr² - 2πrΔr) (l + Δl)

1 = [(πr² - 2πrΔr)/πr²] [(l + Δl)/l]

1 = (1 - Δr/r) (1 + Δl/l)

1 = 1 - (Δr/r) (Δl/l) - Δr/r + Δl/l

(Δr/r) (Δl/l) is the smallest term and hence can be neglected.

So, Δr/r = Δl/l

(Δr/r) / (Δl/l) = 1

which shows that the Poisson's ratio is the ratio of lateral strain to longitudinal strain.

Hence it is 1.