If length of wire is doubled keeping the diameter constant ,its Youngs modulus will be

Y = Stress / Strain = (F / A) / (l / L)   where l is the change in length

Since L is doubled and A remains the same one would expect l, the change in length to also double so Y remains the same.

As an example think of hanging a weight from a spring and the same weight from a similar spring of twice the length - one would expect the longer spring to show twice the extension of the shorter spring.

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