JEE Main & Advanced Physics Transmission of Heat Question Bank Topic Test - Transmission of Heat (3-5-21)

  • question_answer
    The lengths and radii of two rods made of same material are in the ratios 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: 3

    B) 4 : 3

    C) 8 : 9

    D) 3 : 2

    Correct Answer: C

    Solution :

    \[\frac{Q}{t}=\frac{KA({{\theta }_{1}}-{{\theta }_{2}})}{l}\] \[\Rightarrow \] \[\frac{Q}{t}\propto \frac{A}{l}\propto \frac{{{r}^{2}}}{l}\] [As \[({{\theta }_{1}}-{{\theta }_{2}})\] and K are constants]             \[\Rightarrow \frac{{{\left( \frac{Q}{t} \right)}_{1}}}{{{\left( \frac{Q}{t} \right)}_{2}}}=\frac{r_{1}^{2}}{r_{2}^{2}}\times \frac{{{l}_{2}}}{{{l}_{1}}}=\frac{4}{9}\times \frac{2}{1}=\frac{8}{9}\]

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