Question:
The length of a metal wire is $\ell_{1}$, when the tension in it is $T_{1}$ and is $\ell_{2}$ when the tension is $T_{2}$. The natural length of the wire is :
Correct Option: , 2
Solution:
$\mathrm{T}_{1}=\mathrm{k}\left(\ell_{1}-\ell_{0}\right)$
$\mathrm{T}_{2}=\mathrm{k}\left(\ell_{2}-\ell_{0}\right)$
$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\ell_{1}-\ell_{0}}{\ell_{2}-\ell_{0}}$
$\frac{\mathrm{T}_{1} \ell_{2}-\mathrm{T}_{2} \ell_{1}}{\mathrm{~T}_{1}-\mathrm{T}_{2}}=\ell_{0}$