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?