A light spring obeys Hooke's Law. It takes $31\mathrm{.}1$ J of work to stretch this spring from an elongation of $4\mathrm{.}62$ cm to an elongation of $5\mathrm{.}62$ cm$.$

$($a$)$

Is the amount of work required to increase the elongation of the spring from $5\mathrm{.}62$ cm to $6\mathrm{.}62$ cm greater than, less than, or equal to $31\mathrm{.}1$ J$?$

$($b$)$

Verify your answer to part $($a$)$ by calculating the required work $($in J$).$