1 \(T_{1} l_{1}+T_{2} l_{2}\)
2 \(\dfrac{T_{2}}{T_{1}}\left(l_{1}+l_{2}\right)\)
3 \(\dfrac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)
4 \(\dfrac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\)
Explanation:
\(l_{1}=l+\Delta l\)
where \(\quad \Delta l=\dfrac{F}{K}\)
\(K\) is the spring constant
\({l_1} = l + \frac{{{T_1}}}{K}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
\({l_2} = l + \frac{{{T_2}}}{K}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
By eliminating K from eq's (1) & (2)
we get \(\quad l=\dfrac{T_{2} l_{1}-T_{1} l_{2}}{T_{2}-T_{1}}\)