Q. The lengths and radii of two rods made of same material are in the ratios 1:2 and 2:3 respectively. If the temperature difference between the ends for the two rods be the same, then in the steady state, the amount of heat flowing per second through them will be in the ratio
A) 1 : 3
B) 4 : 3
C) 8 : 9
D) 3 : 2
Explanation
(c) $\frac{Q}{t} = \frac{KA(\theta_{1} - \theta_{2})}{l} \Rightarrow \frac{Q}{t} \propto \frac{A}{l} \propto \frac{r^{2}}{l}$
[As $(\theta_{1} - \theta_{2})$ and $K$ are constant]
$\Rightarrow \frac{\left( \frac{Q}{t} \right)_{1}}{\left( \frac{Q}{t} \right)_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} \times \frac{l_{2}}{l_{1}} = \frac{4}{9} \times \frac{2}{1} = \frac{8}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.