Question

Two rods (one semi-circular and other straight) of the same material and the 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 semicircular 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

The correct option is A $2:\pi$

$\frac{dQ}{dt}=\frac{KA\Delta \theta }{l}$, For both rods $K$ and $A\Delta \theta$ are same.
$\Rightarrow \frac{dQ}{dt}\propto \frac{1}{l}$
So, $\frac{{\left(dQ/dt\right)}_{\text{semi circular}}}{{\left(dQ/dt\right)}_{\text{straight}}}=\frac{l_{\text{straight}}}{l_{\text{semi circular}}}=\frac{2r}{\pi r}=\frac{2}{\pi }$