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 temperatures. The ratio of 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$

We know that for semi-circular rod amount of heat generated is given as:

$Q_1=\frac{KA(T_1-T_2)t}{\pi R}$

For straight rod amount of heat generated is given as:

$Q_2=\frac{KA(T_1-T_2)t}{2R}$

So taking there ratio, we find $\frac{Q_1}{Q_2}=\frac{2}{\pi }$