Three conducting rods of same material and cross-section are connected as shown in figure. Temperatures of A, D and C are maintained at \[20{{\,}^{o}}C,\]\[90{{\,}^{o}}C\]and \[0{{\,}^{o}}C.\] If there is no flow of heat in AB, then ratio of the lengths of BC and BD is
A) 2/9
B) 9/2
C) 2/7
D) 7/2
Correct Answer:
C
Solution :
Since there is no flow of heat in rod, so temperature of B is equal to temperature at A i.e., \[{{\theta }_{B}}={{\theta }_{A}}=20{{\,}^{o}}C\] Heat flowing through DB per second = heat flowing through BC per second i.e., \[\frac{KA({{90}^{o}}-{{20}^{o}})}{{{l}_{BD}}}=\frac{KA({{20}^{o}}-{{0}^{o}})}{{{l}_{BC}}}\] \[\therefore \] \[\frac{{{l}_{BC}}}{{{l}_{BD}}}=\frac{2}{7}\]