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AMU Medical AMU Solved Paper-2013

  • question_answer
    Two spheres A and B having radii of 3 cm and 5 cm respectively are coated with carbon black on their outer surfaces. The wavelengths of radiations corresponding to maximum intensity of emission are 300 nm and 500 nm respectivley. The respective powers radiated by them are in the ratio of

    A)  \[\sqrt{\frac{5}{3}}\]                                    

    B)  \[\frac{5}{3}\]

    C)  \[{{\left( \frac{5}{3} \right)}^{2}}\]                         

    D)  \[{{\left( \frac{5}{3} \right)}^{4}}\]

    Correct Answer: D

    Solution :

                     Given that,        \[{{\lambda }_{1}}=300\,nm=3\times {{10}^{-7}}m\]                                 \[{{\lambda }_{2}}=500\,nm\]                                 \[=5\times {{10}^{-7}}m\] We know that                                 \[P\propto {{T}^{4}}\]                 But                         \[T\propto \frac{1}{\lambda }\] So                           \[P\propto {{\left( \frac{1}{\lambda } \right)}^{4}}\]  Then                      \[\frac{{{P}_{1}}}{{{P}_{2}}}={{\left( \frac{{{\lambda }_{2}}}{{{\lambda }_{1}}} \right)}^{4}}={{\left( \frac{5}{3} \right)}^{4}}\]  


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