Q 11-10-027NEETJEE MainEAMCET 2008 (Engineering)Easy
One end of a cylindrical rod is kept in a steam chamber and the other end in melting ice. $0.5$ g of ice melts in $1$ s. If the rod is replaced by another rod of the same length, half the diameter and double the conductivity of the first rod, the rate of melting of ice will be (in g/s)
Answer: (A) $0.25$
Concept. Rate of heat flow $\dfrac{KA\Delta\theta}{l}$, and the rate of melting is proportional to it. Same length and temperatures, so rate $\propto KA$.
Step 1. Factors. Half the diameter gives $\dfrac14$ of the area; double $K$ gives $\times 2$.
Step 2. New rate.
$$0.5 \times \frac14 \times 2 = 0.25\ \text{g/s}$$
Answer. $0.25$ (Option A).
Solution by Sreeraj P, M.Sc Physics