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I have this question.

A sample of wire has a Young modulus E. A second sample of wire made from an identical material has three times the length and half the diameter of the first sample. What is the Young modulus of the second sample of wire in terms of E?

The answer is E. There is no change. Why is this when the stress and strain change by different factors?

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Young's modulus, just like density, specific heat capacity, refractive index etc, is an (intrinsic/intensive) property of the material and independent of the shape and size of the material.

In your example if you increase the length by a factor five and keep all other things equal then the extension will also increase by a factor of five.

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  • $\begingroup$ But wouldn't the area change with diameter meaning the stress would be different? $\endgroup$ Apr 19, 2019 at 8:28
  • $\begingroup$ @OllyScargill The stress will indeed be different but so will the strain in the same proportion so the ratio of stress to strain (Young's modulus) will stay the same. $\endgroup$
    – Farcher
    Apr 19, 2019 at 9:06

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