Question

Two rods (one semi-circular and other straight) of the same material and of same cross-sectional area are joined as shown in the diagram. The points $A$ and $B$ are maintained at different temperatures. 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

• A. $2 : \pi $
• B. $1:2$
• C. $\pi : 2$
• D. $3:2$

Answer 1

Answer: (A)

$\frac{d Q}{d t}=\frac{K A \Delta \theta }{l}$
For both rods $K, A$ and $\Delta \theta $ are same.
$\therefore \frac{d Q}{d t} \propto \frac{1}{l}$
So, $\frac{\left(d Q / d t\right)_{\text{semicircular}}}{\left(d Q / d t\right)_{\text{straight}}}=\frac{l_{\text{straight}}}{l_{\text{semicircular}}}=\frac{2 r}{\pi r}=\frac{2}{\pi }$