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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2004

  • question_answer
    The lengths and radii of two rods made of same material are in the ratio 1:2 and 2:3 respectively. If the temperature difference between the ends for the two rods be the same, then in the steady state, the amount of heat flowing per second through them will be in the ratio

    A)  1 :1                                       

    B)  4 : 3

    C)  8 : 9                                      

    D)  3 : 2

    Correct Answer: C

    Solution :

    For cylindrical rod \[A=\pi {{r}^{2}}\] \[\therefore \] Amount of heat flowing per second                 \[H=\frac{Q}{t}=\frac{KA\Delta \theta }{d}=\frac{K\pi {{r}^{2}}\Delta \theta }{d}\] or            \[H\propto \frac{{{r}^{2}}}{d}\] So,          \[\frac{{{H}_{1}}}{{{H}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}.\frac{{{d}_{2}}}{{{d}_{1}}}\]                 \[={{\left( \frac{2}{3} \right)}^{2}}.\frac{2}{1}=\frac{8}{9}\]


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