# A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by l. Another wire of the same material of length 2L and radius 2r is pulled by a force 2f. Find the increase in length of this wire.

$\frac{l}{\Delta L_2}=\left (\frac{\frac{F_{2}L_{2}}{A_{2}Y_{2}}}{\frac{F_{1}L_{1}}{A_{1}Y_{1}}} \right )=\frac{2f2L}{fL}\times \pi r^{2}\times \frac{Y}{4\pi r^{2}\times Y}$

Hence, , which means the change of length in the second wire is the same.

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