$($a$)$ For a metallic alloy specimen with a uniform cross$-$sectional area of $\backslash (325\backslash$mathrm$\{$~mm$\}^\{2\}\backslash ),$ a gauge length of $115$ mm and a modulus of elasticity of $115$ GPa $,$ if the maximum tensile load at which plastic deformation begins is $\backslash (89,375\backslash$mathrm$\{$~N$\}\backslash ),$ estimate the maximum elastic extension of the specimen.

$(4$ marks$)$