The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio 1:2 are maintained

Q: The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4\;cal/\sec $, that in the shorter rod in $cal/\sec $ will be

a (a) $\frac{{dQ}}{{dt}} = \frac{{K(\pi {r^2})d\theta }}{{dl}}$ ==> $\frac{{{{\left( {\frac{{dQ}}{{dt}}} \right)}_s}}}{{{{\left( {\frac{{dQ}}{{dt}}} \right)}_l}}} = \frac{{{K_s} \times r_s^2 \times {l_l}}}{{{K_l} \times r_l^2 \times {l_s}}}$= $\frac{1}{2} \times \frac{1}{4} \times \frac{2}{1}$ ==> ${\left( {\frac{{dQ}}{{dt}}} \right)_s} = \frac{{{{\left( {\frac{{dQ}}{{dt}}} \right)}_l}}}{4} = \frac{4}{4} = 1$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4\;cal/\sec $, that in the shorter rod in $cal/\sec $ will be

A$1$
B$2$
C$8$
D$16$

Medium

STD 11 Science
NEET
STD 11 - 10.2. transmission of heat
Physics

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