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Root Mean Square Velocity

The length of...

Question

The length of a metal wire is when the tension in it is $T_{1}$ and when the tension in it is $T_{2}$ . The natural length of the wire:

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

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

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

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

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Solution

The correct option is B $\frac{l_{1} T_{2} - T_{1} l_{2}}{T_{2} - T_{1}}$

For $1^{s t}$ case $T_{1} = k (l_{1} - L) \dots (1)$
For $2^{n d}$ case $T_{2} = k (l_{2} - L) \dots (2)$
$(1) \div (2)$
$T_{1} (l_{2} - L) = T_{2} (l_{1} - L)$
$T_{1} l_{2} - T_{1} L = T_{2} l_{1} - T_{2} L$
$L = \frac{l_{1} T_{2} - T_{2} l_{2}}{T_{2} - T_{1}}$

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