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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

  • question_answer
    The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio 1:2 and their lengths are in the ratio 2 : 1. If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be

    A)  1 : 4             

    B)  1 : 2

    C)  1 : 8             

    D)  1 : 3

    Correct Answer: C

    Solution :

     \[H=\frac{KA\Delta \theta }{l}\] or            \[H\propto \frac{{{r}^{2}}}{l}\] so, \[\frac{{{H}_{1}}}{{{H}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\left( \frac{{{I}_{2}}}{{{I}_{1}}} \right)\] \[={{\left( \frac{1}{2} \right)}^{2}}\left( \frac{1}{2} \right)\] \[=\frac{1}{8}\] \[\Rightarrow \] \[{{H}_{1}}:{{H}_{2}}=1:8\]


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