Multiple$-$Concept Example $4$ reviews the concepts that are involved in this problem. A ruler is accurate when the temperature is $29\mathrm{.}8$

$$C$.$ When the temperature drops to $-13\mathrm{.}5$C$,$ the ruler shrinks and no longer measures distances accurately. However, the ruler can be made to read correctly if a force of magnitude $1\mathrm{.}71$ x $103$ N is applied to each end so as to stretch it back to its original length. The ruler has a cross$-$sectional area of $1\mathrm{.}30$ x $10-5$ m$2,$ and it is made from a material whose coefficient of linear expansion is $2\mathrm{.}5$ x $10-5($C$)-1.$

What is Young's modulus for the material from which the ruler is made?