To solve this problem we will apply the concept related to the Poisson ratio for which the longitudinal strains are related, versus the transversal strains. Â First we need to calculate the longitudinal strain as follows
[tex]\epsilon_x = \frac{l_f-l_i}{l_i}[/tex]
[tex]\epsilon_x = \frac{(9.80554)-(9.8)}{9.8}[/tex]
[tex]\epsilon_x = 0.0005653[/tex]
Second we will calculate the lateral strain as follows
[tex]\epsilon_y = \frac{a_f-a_i}{a_i}[/tex]
[tex]\epsilon_y = \frac{2.59952-2.6}{2.6}[/tex]
[tex]\epsilon_y = -0.0001846153[/tex]
The Poisson's ratio is the relation between the two previous strain, then,
[tex]\upsilon = -\frac{\epsilon_y}{\epsilon_x}[/tex]
[tex]\upsilon = -\frac{(-0.0001846153)}{0.0005653}[/tex]
[tex]\upsilon = 0.3265[/tex]
Therefore the Poisson's ratio for the material is 0.3265
