When a $4\mathrm{.}70-$kg object is hung vertically on a certain light spring that obeys Hooke's law, the spring stretches $2\mathrm{.}80$ cm$.$

$($a$)$ If the $4\mathrm{.}70-$kg object is removed, how far will the spring stretch if a $1\mathrm{.}50-$kg block is hung on it$?$

$0\mathrm{.}893$ cm

$($b$)$ How much work must an external agent do to stretch the same spring $4\mathrm{.}00$ cm from its unstretched position?

$1\mathrm{.}316$ J