Q. The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio 1:2 and their lengths are in the ratio 2:1. If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be
A) 1 : 1
B) 2 : 1
C) 1 : 4
D) 1 : 8
Explanation
(d) $\frac{Q}{t} = \frac{KA\mathrm{\Delta}\theta}{l} \Rightarrow \frac{Q}{t} \propto \frac{A}{l} \propto \frac{d^{2}}{l}\ \lbrack d =$ diameter of rod]
$\Rightarrow \frac{(Q/t)_{1}}{(Q/t)_{2}} = \left( \frac{d_{1}}{d_{2}} \right)^{2} \times \frac{l_{2}}{l_{1}} = \left( \frac{1}{2} \right)^{2} \times \left( \frac{1}{2} \right) = \frac{1}{8}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.