A $100-$mm$-$long rod has a diameter of $15mm.$ If an axial tensile load of $10kN$ is applied to it$,$ the change in its diameter is most nearly? Assume the material behaves elastically and the Elastic modulus $=70$GPa and Poisson's ratio $=0\mathrm{.}35.$

$-4{10}^{-4}mm$

$-4{10}^{-3}mm$

$-4{10}^{-2}mm$

$-4{10}^{-5}mm$

$-4{10}^{-6}mm$