$5\mathrm{.}4$ A close$-$coiled helical spring having n coils of steel wire and a mean diameter D $,$ which is eight times the diameter $d$ of the wire, has a stiffness of $\frac{d}{n}$ constant $\frac{N}{m}.$ Calculate $($a$)$ the value of the constant; $($b$)$ the diameter of the wire for a spring having $10$ turns and a stiffness of $8,69k\frac{N}{m}$; and $($c$)$ the stress in the wire for a load of $)=(80$GPa.

$19,5{10}^6$;$4,45(mm)$;$342,68$MPa