$A$ copper rod of length $75 \ cm$ and an iron rod of length $125 \ cm$ are joined together end to end. Both are of circular cross-section with diameter $2 \ cm$. The free ends of the copper and iron are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The surfaces of the bars are insulated thermally. The temperature of the copper-iron junction is (Thermal conductivity of copper is $386.4 \ W/m-K$ and thermal conductivity of iron is $48.46 \ W/m-K$) (in $^{\circ} C$)
- A$100$
- B$0$
- C$93$
- D$50$
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