Railways Technical Ability Vibration Analysis Question Bank Vibration Analysis

  • question_answer Two spheres A and B of same material have radii 1 m and 4 m and temperature 4000 K and 2000 K respectively. Which one of the following statements is correct? The energy radiated by sphere A is:

    A) Greater than that of sphere B

    B) Less than that of sphere B

    C) Equal to that of sphere B

    D) Equal to double that of sphere B

    Correct Answer: C

    Solution :

    \[\frac{{{E}_{A}}}{{{E}_{B}}}=\left( \frac{{{A}_{A}}}{{{A}_{B}}} \right)\,\,{{\left( \frac{{{T}_{A}}}{{{T}_{B}}} \right)}^{4}}\] \[={{\left( \frac{{{A}_{A}}}{{{r}_{B}}} \right)}^{2}}{{\left( \frac{{{T}_{A}}}{{{T}_{B}}} \right)}^{4}}\] \[={{\left( \frac{1}{4} \right)}^{2}}{{\left( \frac{4000}{2000} \right)}^{4}}=1\]

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