A cylindrical metal specimen $12\mathrm{.}7$ mm $(0\mathrm{.}5$ in$.)$ in diameter and $250$ mm $(10$ in$.)$ long is to be subjected to a tensile stress of $28$ MPa $(4000$ psi; at this stress level, the resulting deformation will be totally elastic.a$.$ If the elongation must be less than $0\mathrm{.}080$ mm $(3\mathrm{.}2\backslash$times $10-3$ in$.),$ which of the metals in Table $6\mathrm{.}1$ are suitable candidates? Why?b$.$ If$,$ in addition, the maximum permissible diameter decrease is $1\mathrm{.}2\backslash$times $10-3$ mm $(4\mathrm{.}7\backslash$times $10->$ in$.)$ when the tensile stress of $28$ MPa is applied, which of the metals that satisfy the criterion in part $($a$)$ are suitable candidates? Why?