What force is required to stretch a steel wire of cross-sectional area $1\;cm^2$ to double its length?

Given,
Area of the cross-section $(A) = 1\;cm^2 = 1 * 10^{-4}\,m$
Young's modulus of steel $(Y) = 2 * 10^{11}\,N/m^2$
Let, length of the wire $(l) = x\;cm$
After extension its length $(L)$ becomes double       i.e   $2x$
So extension $(e) = \Delta l = L - l = 2x - x = x\;cm$
Force $(F) = ?$

Now we have,

$Y = \frac{F/A}{e/l} = \frac{F/A}{x/x} = \frac{F}{A}$

⇒ $F = Y\,*\,A = 2 * 10^{11} \; * \; 1 \; * \; 10^{-4} = 2 * 10^{7}\;N$

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