Question

a metal wire of length 2 m get elongated by 2 mm under a given lad if initial diameter is 1mm find change in diameter taking poison ratio to be 0.24​

Answer 1

Answer:

Explanation: Given:

L= original length of wire = 2m

l = Elongation in wire = 2mm = 2x$10^{-3}$ m

D = dia of wire = 1mm = 1x$10^{-3}$ m

σ = 0.24

To calculate: change in diameter of wire

we know

longitudinal strain = I/L = 1x$10^{-3}$m

Poisons ratio = lateral strain / longitudinal strain

lateral strain = 0.24x 1x$10^{-3}$ = 0.24 x$10^{-3}$ and lateral strain = d/D

thus ,

d = Dxlateral strain = 1x$10^{-3}$x 0.24 x$10^{-3}$ =  0.24 x$10^{-6}$m

Ans: Thus change in diameter is  0.24 x$10^{-6}$m