Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points $A$ and $B$ are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time is
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(a) $\frac{{dQ}}{{dt}} = \frac{{KA\Delta \theta }}{l}$, For both rods $K, A$ and $\Delta$ $\theta$ are same
==> $\frac{{dQ}}{{dt}} \propto \frac{1}{l}$ So $\frac{{{{(dQ/dt)}_{semi\,circular}}}}{{{{(dQ/dt)}_{straight}}}} = \frac{{{l_{straight}}}}{{{l_{semicircular}}}} = \frac{{2r}}{{\pi \,r}} = \frac{2}{\pi }$.
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