Physics - Elasticity Question with Solution | TestHub

Assuming Hooke's law to be valid

$T\propto \left(\Delta \ell \right)$

$T=k\left(\Delta \ell \right)$

Let,${\ell }_0=$ natural length (original length) $\Rightarrow T=k\left(\ell -{\ell }_0\right)$

so, $T_1=k\left({\ell }_1-{\ell }_0\right) \& T_2=k\left({\ell }_2-{\ell }_0\right)$

$\Rightarrow \frac{T_1}{T_2}=\frac{{\ell }_1-{\ell }_0}{{\ell }_2-{\ell }_0}$

$\Rightarrow {\ell }_0=\frac{T_2{\ell }_1-T_1{\ell }_2}{ T_2-T_1}$