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In this question:

The Young modulus of steel is determined using a length of steel wire and is found to have the value $E$. Another experiment is carried out using a wire of the same steel, but of half the length and half the diameter.

What value is obtained for the Young modulus in the 2nd experiment?

I know that the Young's modulus is an intrinsic property of a object. But what I found confusing is that, when I calculated the Young's modulus for the 2nd experiment, I got $2E$. But the answer was $E$, instead of $2E$.

However, my thought kept lying with the equation: $$\text{Young's modulus} = \frac{\text{force}\times\text{length}}{\text{extension}\times\text{area}}$$

Doesn't the change in length and diameter affect the Young's modulus value? How can it be an intrinsic value for a object?

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2 Answers 2

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From the given information how did you "calculate the Young's modulus for the 2nd experiment"?
You cannot assume that in the second experiment the force and extension are the same as in the first experiment because they are not.
For a given force the extension would be twice in the second experiment as that in the first experiment.

Update in response to a comment

$\text{extension}_1 = \dfrac{\text{force}\times\text{length}}{\text{Young's modulus}\times\text{area}}$

$\text{extension}_2 = \dfrac{\text{force}\times\frac{\text{length}}{2}}{\text{Young's modulus}\times\frac{\text{area}}{4}}=2\times \text{extension}_1$

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  • $\begingroup$ For a given amount force extension is half in the 2nd case.Can you please elaborate on this? $\endgroup$
    – Paul
    Jan 31, 2017 at 6:48
  • $\begingroup$ @Theasgardian Correction made. $\endgroup$
    – Farcher
    Jan 31, 2017 at 6:53
  • $\begingroup$ I think the extension should be same not twice or half because both lenght and diameter has decreased. $\endgroup$
    – Paul
    Jan 31, 2017 at 6:57
  • $\begingroup$ @Theasgardian I have updated my answer. $\endgroup$
    – Farcher
    Jan 31, 2017 at 7:10
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This question was asked about 3 years ago and by now, you might have passed the A Levels too so this answer might seem irrelevant to you now. But as it turns out, I was having the same problem with the exact question and was seeking the same answer as you did.

I finally found it and wanted to share with you and I hope this will help anyone else who is facing the same problem.

This is just a very stupid question that only has one explanation. It is a fact. The Young Modulus of Steel is between 190 to 215 GPa according to Google. No matter how you change the length and diameter and force, it will always stay constant. The reason is because if you increase force or diameter, the value of stress will increase and so will the expansion and the strain. No matter what variable you change (except for the material), the ratio will always stay the same. To prove this you will need experimental values and mathematics beyond the A Level syllabus.

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