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Structure of Glucose

The length of...

Question

The length of metallic wire is $l_{1}$ when the tension is $T_{1}$ and $l_{2}$ when the tension is $T_{1}$ . The original length of the wire is

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

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

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

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\sqrt{T_{1} T_{2} l_{1} l_{2}}

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Solution

The correct option is C $\frac{l_{1} T_{2} - l_{2} T_{1}}{T_{2} - T_{1}}$
$l_{1} = l + x_{1}$
$l_{2} = l + x_{2}$
$T_{1} = \frac{Y A}{l} x_{1}$
$T_{2} = \frac{Y A}{l} x_{2}$
$\frac{T_{1}}{T_{2}} = \frac{x_{1}}{x_{2}} = \frac{l_{1} - l}{l_{2} - l}$
$T_{1} l_{2} - T_{1} l = T_{2} l_{1} - T_{2} l$
$l = \frac{T_{2} l_{1} - T_{1} l_{2}}{T_{2} - T_{1}}$

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