The Young modulus is given by:
[tex]E= \frac{F /A}{\Delta L / L_0} [/tex]
where
F is the force applied
[tex]L_0[/tex] is the initial length of the wire
[tex]A[/tex] is the cross-sectional area of the wire
[tex]\Delta L[/tex] is the stretch of the wire
The wire in the problem stretches by [tex]0.5%[/tex] of its length, this means
[tex] \frac{\Delta L}{L_0} = 0.005[/tex]
We can also calculate the area of the wire; its radius is in fact half the diameter:
[tex]r= \frac{d}{2}= \frac{0.600 mm}{2}=0.300 mm=0.3 \cdot 10^{-3} m [/tex]
and so the area is
[tex]A=\pi r^2 = \pi (0.3 \cdot 10^{-3} m)^2 = 2.83 \cdot 10^{-7} m^2[/tex]
We know the force applied to the wire, F=20 N, so now we have everything to calculate the Young modulus:
[tex]E= \frac{F/A}{\Delta L / L_0} = \frac{20 N/(2.83 \cdot 10^{-7} m^2)}{0.005}=1.42 \cdot 10^{10} N/m^2 [/tex]
