Question

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 :

• 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 $K,A$ and $\Delta \theta$ are same

$\frac{dQ}{dt}\propto \frac{1}{l}$

so, $\frac{{\left(dQ/dt\right)}_{semicircular}}{{\left(dQ/dt\right)}_{straight}}=\frac{l_{straight}}{l_{semicircular}}=\frac{2r}{\pi r}=\frac{2}{\pi }$