The Young modulus of steel is two times that of copper. A $50\,\text{cm}$ length of copper wire with diameter $2.0\,\text{mm}$ is joined onto a $50\,\text{cm}$ length of steel wire with diameter $1.0\,\text{mm}$, forming a combined wire of length $1.0\,\text{m}$, as illustrated. The combined wire is stretched by a weight attached at its end. Both the copper wire and the steel wire obey Hooke’s law. What is the ratio $\frac{\text{extension of steel wire}}{\text{extension of copper wire}}$ ?
- A$4$
- B$2$
- C$1$
- D$0.5$