JIPMER Jipmer Medical Solved Paper-2008

  • question_answer
    The speed of earths rotation about its axis is\[\omega .\]Its speed is increased to x times to make the effective acceleration due to gravity equal to zero at the equator. Then x is

    A) 1                                             

    B) 8.5                         

    C) 17                          

    D)        34

    Correct Answer: C

    Solution :

    Earth rotates about its own axis in 24 h. So,       \[T=24\times 60\times 60\,s\] So, angular speed of earth about its own axis \[\omega =\frac{2\pi }{T}=\frac{2\pi }{24\times 60\times 60}rad\text{/}s\] At equator,  \[g=g-{{R}_{e}}\omega {{}^{2}}\] or            \[0=g-{{R}_{e}}\omega {{}^{2}}\] or            \[\omega =\sqrt{\frac{g}{{{R}_{e}}}}=\frac{2\pi }{84.6\times 60}\] \[\therefore \]  \[\frac{\omega }{\omega }=\frac{24\times 60\times 60}{84.6\times 60}\approx 17\] \[\Rightarrow \]               \[\omega =17\,\omega \] So, value of x is 17.


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