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

Answer: (A)

2 :$\pi$

Answer 2

$\frac{dQ}{dt} = \frac{KA\Delta\theta}{l}$, For both rods K, A and ∆θ are same

∴ $\frac{dQ}{dt} \propto \frac{1}{l}$

So $\frac{(dQ/dt)_{semicircular}}{(dQ/dt)_{straight}} = \frac{l_{straight}}{l_{semicircular}} = \frac{2r}{\pi r} = \frac{2}{\pi}$.