question_answer

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at \[{{0}^{o}}C\] and \[{{90}^{o}}C\] respectively. The temperature of the junction of the three rods will be [IIT-JEE (Screening) 2001]

A)            \[{{45}^{o}}C\]

B)            \[{{60}^{o}}C\]

C)            \[{{30}^{o}}C\]

D)            \[{{20}^{o}}C\]

Correct Answer: B

Solution :

                   Let the temperature of junction be q. Since roads B and C are parallel to each other (because both having the same temperature difference). Hence given figure can be redrawn as follows Q \[\frac{Q}{t}=\frac{({{\theta }_{1}}-{{\theta }_{2}})}{R}\] and \[{{\left( \frac{Q}{t} \right)}_{AB}}={{\left( \frac{Q}{t} \right)}_{BC}}\] Þ \[\frac{(90-\theta )}{R/2}=\frac{(\theta -0)}{R}\] Þ \[180-2\theta =\theta \] Þ\[\theta =60{}^\circ C\]