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CMC Medical CMC-Medical Ludhiana Solved Paper-2009

  • question_answer
    Two solid spheres A and B made of the same material have radii\[{{r}_{A}}\]and\[{{r}_{B}}\]respectively. Both the spheres are cooled from the same temperature under the conditions valid (or Newtons law of cooling. The ratio of the rate of change of temperature A and B is

    A)  \[\frac{{{r}_{A}}}{{{r}_{B}}}\]                                    

    B)  \[\frac{{{r}_{B}}}{{{r}_{A}}}\]

    C)  \[\frac{{{r}_{A}}}{{{r}_{B}}^{2}}\]                                            

    D)  \[\frac{{{r}_{B}}^{2}}{{{r}_{A}}^{2}}\]

    Correct Answer: B

    Solution :

                    \[\frac{4\pi }{3}{{r}^{3}}\rho c\left( -\frac{dT}{dt} \right)=\sigma 4\pi {{r}^{2}}\left( {{T}^{4}}-T_{0}^{4} \right)\] \[\therefore \]  \[\left( -\frac{dT}{dt} \right)=\frac{3\sigma }{\rho rc}\left( {{T}^{4}}-T_{0}^{4} \right)=H\]     (say) Ratio of rates of fall of temperature \[\frac{{{H}_{A}}}{{{H}_{B}}}=\frac{{{r}_{B}}}{{{r}_{A}}}\]


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