A rod of length 'λ' and cross-section
'A' is used to melt a piece of ice as shown.
Now if the rod broken into two equal parts and is arranged as shown. Time taken to melt ice in second case becomes.

Question

A rod of length 'λ' and cross-section 'A' is used to melt a piece of ice as shown. Now if the rod broken into two equal parts and is arranged as shown. Time taken to melt ice in second case becomes.

G1 Physics · Accepted Answer

In steady conduction, heat current is H=kAΔT/L. Treat each segment as a thermal resistance Rₜₕ=L/(kA); series resistances add and parallel heat currents add. Evaluating the given data/statements gives B: One-forth. Therefore the correct answer is B.