Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2011

  • question_answer
    The time period of rotation of the sun is 25 days and its radius \[7\times {{10}^{8}}m.\] The Doppler shift for the light of wavelength \[6000\,\overset{\text{o}}{\mathop{\text{A}}}\,\] emitted from the surface of the sun will be

    A) \[0.04\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[0.40\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[4.00\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[40.0\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    Correct Answer: A

    Solution :

    Doppler's shift, \[\Delta \lambda =\frac{v}{c}\lambda \] \[\Delta \lambda =\frac{r\omega }{c}\lambda \]               ( \[\because \] \[v=r\omega \]) \[\Delta \lambda =\frac{r\lambda }{c}\left( \frac{2\pi }{T} \right)\]                           \[\left( \because \,\omega =\frac{2\pi }{T} \right)\] \[\Delta \lambda =\frac{7\times {{10}^{8}}\times 6000\times 2\times 3.14}{3\times {{10}^{8}}\times 25\times 24\times 3600}\overset{\text{o}}{\mathop{\text{A}}}\,=0.04\overset{\text{o}}{\mathop{\text{A}}}\,\]


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