A $23\mathrm{.}0$ cm long spring is hung vertically from a ceiling and stretches to $30\mathrm{.}9$ cm when an $8\mathrm{.}00$ kg mass is hung from its free end. $($a$)$ Find the spring constant $($in N$/$m$).$ N$/$m $($b$)$ Find the length of the spring $($in cm$)$ if the $8\mathrm{.}00$ kg weight is replaced with a $205$ N weight. cm