\(T \propto(\Delta \ell)\)

\(T = k (\Delta \ell)\)

Let, \(\ell_{0}=\) natural length (original length)

\(\Rightarrow T = k \left(\ell-\ell_{0}\right)\)

so, \(T _{1}= k \left(\ell_{1}-\ell_{0}\right)\) And \(T _{2}= k \left(\ell_{2}-\ell_{0}\right)\)

\(\Rightarrow \frac{ T _{1}}{ T _{2}}=\frac{\ell_{1}-\ell_{0}}{\ell_{2}-\ell_{0}}\)

\(\Rightarrow \ell_{0}=\frac{ T _{2} \ell_{1}- T _{1} \ell_{2}}{ T _{2}- T _{1}}\)