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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 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is ______ cm.

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answer is 5.

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Detailed Solution

$\begin{array}{l} {Δℓ}_{1} = \frac{Fℓ}{AY} = \frac{Fℓ}{{πr}^{2} Y} = 5 cm \\ {Δℓ}_{2} = \frac{4 F 4 ℓ}{π 16 r^{2} Y} = \frac{Fℓ}{{πr}^{2} Y} = 5 cm \end{array}$

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