Example Problem $8\mathrm{.}2$: $($p$\mathrm{.}219)$

A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of $10$ mm $.$ Determine the magnitude of the load required to produce a $2\mathrm{.}5{10}^{-3}$ mm change in diameter if the deformation is entirely elastic.

$d_0=10mm$

$d=2\mathrm{.}5{10}^{-3}mm$

$V_{\text{b}\text{r}\text{a}\text{s}\text{s}}=0\mathrm{.}34($from table $8\mathrm{.}1)$

$E_{\text{b}\text{r}\text{a}\text{s}\text{s}}=97$GPa $($from table $8\mathrm{.}1)$

$P=?$