The length of a metal wire is $l_{1}$ when the tension in it is $F_{1}$ and $l_{2}$ when the tension is $F_{2}$ . Then original length of the wire is:

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

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\frac{l_{2} - l_{1}}{F_{2} - F_{1}}

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\frac{l_{1} F_{2} - l_{2} F_{1}}{F_{1} - F_{2}}

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\frac{l_{1} F_{1} - l_{2} F_{2}}{F_{2} - F_{1}}

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Solution

The correct option is C $\frac{l_{1} F_{2} - l_{2} F_{1}}{F_{1} - F_{2}}$

$F \propto Δ l$

$F_{1} \propto l_{1} - l$
Where $l$ , is the original length of the wire

$F_{2} \propto l_{2} - l$

$\frac{F_{1}}{F_{2}} = \frac{l_{1} - l}{l_{2} - l}$

$F_{1} l_{2} - F_{1} l = F_{2} l_{1} - F_{2} l$

$(F_{2} - F_{1}) l = F_{2} l_{1} - F_{1} l_{2}$

$l = \frac{F_{2} l_{1} - F_{1} l_{2}}{F_{2} - F_{1}}$

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