When the tension in a metal wire is $F_{1}$ its length is $L_{1}$ and then the tension in the wire is $F_{2}$ the length is $L_{2}$ . The natural length of the wire is

L_{1} F_{2} = L_{2} F_{1}

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\frac{L_{1} F_{2} + L_{2} F_{1}}{F_{2} + F_{1}}

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\frac{L_{1} F_{2} - L_{2} F_{1}}{F_{2} + F_{1}}

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L_{1} F_{1} + L_{2} F_{2}

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Solution

The correct option is C $\frac{L_{1} F_{2} - L_{2} F_{1}}{F_{2} + F_{1}}$
$\begin{matrix} Y = \frac{F \cdot L}{A Δ L} Y & = \frac{F_{1} L}{A \cdot (L_{1} - L)} T & = \frac{F_{2} L}{A (L_{2} - L)} \end{matrix}$
$\frac{F_{1}}{L_{1} - L} = \frac{F_{2}}{L_{2} - L}$
$L = \frac{L_{1} F_{2} - L_{2} F_{1}}{F_{2} - F_{1}}$

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