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