When the tension on a wire is 4N its length is $l_1$ . When the tension on the wire is 5N its length is $l_2$. Find its natural length.

$\text{ When'}{\mathrm{F}}_1\text{'is applied }\to \text{ length is '}{l}_1\text{'}$

$\mathrm{When}\text{'}{\mathrm{F}}_2\text{'}\text{ is applied }\to \text{ length'}{l}_2\text{' }$

Let its natural length  ${ }^{\text{'}}{l}^{\text{'}},\mathrm{e}=\frac{\mathrm{Fl}}{\mathrm{AY}}$

$\left({\mathrm{l}}_1-\mathrm{l}\right)=\frac{{\mathrm{F}}_1\mathrm{l}}{\mathrm{AY}}\dots .\left(1\right);\left({\mathrm{l}}_2-\mathrm{l}\right)=\frac{{\mathrm{F}}_2\mathrm{l}}{\mathrm{AY}}....\left(2\right)$

from (1) and (2) we get

$l=\frac{l_1{\mathrm{F}}_2-l_2{\mathrm{F}}_1}{{\mathrm{F}}_2-{\mathrm{F}}_1}$