question_answer

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 \[i.e.,\] \[\frac{KA({{90}^{o}}-{{20}^{o}})}{{{I}_{BD}}}=\frac{KA({{20}^{o}}-{{0}^{o}})}{{{I}_{BC}}}\] \[\therefore \]  \[\frac{{{I}_{BC}}}{{{I}_{BD}}}=\frac{2}{7}\]