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BHU PMT BHU PMT (Screening) Solved Paper-2005

  • question_answer
    Earth is revolving around the sun. If the distance of the earth from the sun is reduced to 1/4th of the present distance, then the length of present day will be reduced by:

    A)  1/4                                       

    B)  ½

    C)   1/8                                      

    D)  1/6

    Correct Answer: C

    Solution :

                     From Kepler?s third law of planetary motion, the square of period of revolution of any planet around the sun is directly proportional to the cube of the semi-major axis of its elliptical orbit. \[{{T}^{2}}\propto {{a}^{3}}\] Given, \[a'=\frac{a}{4}\] \[\therefore \]  \[\frac{{{T}^{2}}}{T{{'}^{2}}}=\frac{{{a}^{3}}}{{{\left( \frac{a}{4} \right)}^{3}}}={{(4)}^{3}}\] \[\Rightarrow \]               \[T'=\frac{T}{{{(4)}^{3/2}}}=\frac{T}{8}\]


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