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

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

$\frac{T_{2} l_{1} - T_{1} l_{2}}{T_{1} + T_{2}}$

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

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

answer is D.

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Detailed Solution

$T α Δ l [∵ T = K Δ l] ∴ \frac{T_{1}}{T_{2}} = \frac{l_{1} - l_{0}}{l_{2} - l_{0}} o r, T_{1} l_{2} - T_{2} l_{0} = T_{2} l_{1} - T_{2} l_{0} ∴ l_{0} = \frac{T_{2} l_{1} - T_{1} l_{2}}{T_{2} - T_{1}}$

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