A metal bar with a rectangular cross$-$section $0\mathrm{.}02$ m x $0\mathrm{.}04$ m and a gauge length of $0\mathrm{.}40$ m is subjected to

a centric tensile load of $400$ kN$.$ After the load is applied, the $0\mathrm{.}02$ m dimension changed to $0\mathrm{.}01998$ m

and the $0\mathrm{.}40$ m gauge length changed to $0\mathrm{.}402$ m$.$ If the behavior of the material is assumed to be within

the proportionality range between stress and strain, determine:

a$)$ Poisson$$s ratio for this material;

b$)$ the final value of the $0\mathrm{.}04$ m dimension;

c$)$ the average normal stress in the bar;

d$)$ the maximum shear stress in the bar;

e$)$ the modulus of elasticity of the metal. What engineering material could it be$?$A metal bar with a rectangular cross$-$section $0\mathrm{.}02mx0\mathrm{.}04m$ and a gauge length of $0\mathrm{.}40m$ is subjected to

a centric tensile load of $400kN.$ After the load is applied, the $0\mathrm{.}02m$ dimension changed to $0\mathrm{.}01998m$

and the $0\mathrm{.}40m$ gauge length changed to $0\mathrm{.}402m.$ If the behavior of the material is assumed to be within

the proportionality range between stress and strain, determine:

a$)$ Poisson's ratio for this material;

b$)$ the final value of the $0\mathrm{.}04m$ dimension;

c$)$ the average normal stress in the bar;

d$)$ the maximum shear stress in the bar;

e$)$ the modulus of elasticity of the metal. What engineering material could it be$?$