Transmission Of Heat Question 58
Question: The ratio of the diameters of two metallic rods of the same material is 2 : 1 and their lengths are in the ratio 1 : 4. If the temperature difference between their ends are equal, the rate of flow of heat in them will be in the ratio
[MP PET 1994]
Options:
A) 2 : 1
B) 4 : 1
C) $ 8:1 $
D) 16 : 1
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{Q}{t}=\frac{kA(\Delta \theta )}{l} $
Therefore $ \frac{Q}{t}\propto \frac{A}{l}\propto \frac{r^{2}}{l} $
Therefore $ \frac{{{( Q/t )}_1}}{{{(Q/t)}_2}}$=
${{( \frac{r _{1}}{r _{2}} )}^{2}}\times \frac{l _{2}}{l _{1}} $
$ ={{( \frac{2}{1} )}^{2}}\times ( \frac{4}{1} )=\frac{16}{1} $
BETA
