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 :
• B. 1 : 2
• C. p : 2
• D. 3 : 2

Answer 1

The correct option is A

2 :

$\frac{dQ}{dt}=\frac{KA△\theta }{l}$,
For both rods K, A and $△\theta$ are same
$\Rightarrow \frac{dQ}{dt}\propto \frac{1}{l}so\frac{(\frac{dQ}{dt}{)}_{semicircular}}{(\frac{dQ}{dt}{)}_{straight}}=\frac{l_{straight}}{l_{semicircular}}=\frac{2r}{\pi r}=\frac{2}{\pi }$.