The length of metallic wire


The length of metallic wire is $l_{1}$ when tension in it is $T_{1}$. It is $l_{2}$ when the tension is $T_{2}$. The original length of the wire will be :

  1. $\frac{l_{1}+l_{2}}{2}$

  2. $\frac{\mathrm{T}_{1} l_{1}-\mathrm{T}_{2} l_{2}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$

  3. $\frac{\mathrm{T}_{2} l_{1}+\mathrm{T}_{1} l_{2}}{\mathrm{~T}_{1}+\mathrm{T}_{2}}$

  4. $\frac{T_{2} l_{1}-T_{1} l_{2}}{T_{2}-T_{1}}$

Correct Option: , 4



From young's modulus relation $\left(\mathrm{y}=\frac{\frac{\mathrm{F}}{\mathrm{A}}}{\left(\frac{\Delta \mathrm{I}}{\mathrm{I}}\right)}\right)$

we can write for $1^{\text {st }}$ case


we can write for $2^{\text {nd }}$ case



$\mathrm{T}_{1} \ell_{2}-\mathrm{T}_{1} \ell=\mathrm{T}_{2} \ell_{1}-\mathrm{T}_{2} \ell$

$\frac{T_{2} l_{1}-T_{1} l_{2}}{T_{2}-T_{1}}=\ell$


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