A metallic rod $($initial diameter $\backslash (=50\backslash$mathrm$\{$~mm$\}\backslash ),$ initial length $\backslash (=100\backslash$mathrm$\{$~mm$\}\backslash ))$ is subjected to a $2000$ kN load. The resulting dimensions after the load has been applied are the final diameter $\backslash (=45\backslash$mathrm$\{$~mm$\}\backslash )$ and the final length $\backslash (=105\backslash$mathrm$\{$~mm$\}\backslash ).$

a$.$ Calculate the normal stress experienced by the rod, assuming linear elastic behavior. Provide your final answer in MPa. $(1$pt$)$

b$.$ Calculate the elastic modulus, assuming linear elastic behavior. Provide your final answer in GPa. $(1$pts$)$

c$.$ Calculate the Poisson's ratio, assuming linear elastic behavior. $(0\mathrm{.}25$pts$)$