$A$ structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. $A$ $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress,$(b)$ elongation,and $(c)$ strain on the rod. Young's modulus of structural steel is $2.0 \times 10^{11} \;N \;m^{-2}$.

(N/A) Given: Radius $r = 10 \;mm = 10^{-2} \;m$,Length $L = 1.0 \;m$,Force $F = 100 \;kN = 10^5 \;N$,Young's modulus $Y = 2.0 \times 10^{11} \;N \;m^{-2}$.
$(a)$ Stress: $\text{Stress} = \frac{F}{A} = \frac{F}{\pi r^2} = \frac{10^5 \;N}{3.14 \times (10^{-2} \;m)^2} = \frac{10^5}{3.14 \times 10^{-4}} \approx 3.18 \times 10^8 \;N \;m^{-2}$.
$(b)$ Elongation: Using $\Delta L = \frac{FL}{AY}$,we have $\Delta L = \frac{\text{Stress} \times L}{Y} = \frac{3.18 \times 10^8 \;N \;m^{-2} \times 1.0 \;m}{2.0 \times 10^{11} \;N \;m^{-2}} = 1.59 \times 10^{-3} \;m = 1.59 \;mm$.
$(c)$ Strain: $\text{Strain} = \frac{\Delta L}{L} = \frac{1.59 \times 10^{-3} \;m}{1.0 \;m} = 1.59 \times 10^{-3} = 0.159 \% \approx 0.16 \%$.