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AMU Medical AMU Solved Paper-2014

  • question_answer
    Two spherical bodies P (radius 9 cm) and Q (radius 27 cm) are at temperatures \[{{T}_{p}}\] and \[{{T}_{Q}}\]respectively. If the maximum intensities in the emission spectra of P and Q are, respectively, at 300 nm and 900 nm, what is the ratio of the rate of energy radiated by P to that by Q?

    A)  6                                            

    B)  7     

    C)  8                                            

    D)  9

    Correct Answer: D

    Solution :

                     The given,                 \[{{r}_{1}}=9\,cm\]                 \[{{r}_{2}}=27\,cm\]                 \[{{\lambda }_{p}}=300\,nm\]                 \[{{\lambda }_{Q}}=900\,nm\] So, the ratio of the rate of energy radiated                 \[\frac{{{Q}_{1}}}{{{Q}_{2}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}{{\left( \frac{{{\lambda }_{Q}}}{{{\lambda }_{p}}} \right)}^{4}}\]                 \[=\frac{9\times 9}{27\times 27}\times {{\left( \frac{900}{300} \right)}^{4}}\]                 \[=\frac{9}{3\times 27}\times \frac{9\times 9\times 9\times 9}{3\times 3\times 3\times 3}\]                 \[=\frac{9}{1}=9:1\]or = 9


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