The length of a metal bar is 20 cm and the area of cross section is \(4 \times 10^{-4} \mathrm{~m}^2\). If one end of the rod is kept in ice at \(0^{\circ} \mathrm{C}\) and the other end is kept in steam at \(100^{\circ} \mathrm{C}\), the mass of ice melted in one minute is 5 g . The thermal conductivity of the metal in \(\mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) is (Latent heat of fusion \(=80 \mathrm{cal} / \mathrm{gm}\) )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.