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9th Class Science Gravitation and Floatation Question Bank Gravitation

  • question_answer
    The height at which the acceleration due to gravity becomes g/9 (where g is the acceleration due to gravity on the surface of the Earth) in terms of R, the radius of the Earth is

    A) 2R                               

    B) \[R/\sqrt{2}\]  

    C) \[R/2\] 

    D)        \[\sqrt{2}/R\]              

    Correct Answer: A

    Solution :

    We know, \[g=\frac{GM}{{{R}^{2}}}\] \[g'=\frac{g}{9}=\frac{GM}{9{{R}^{2}}}\]                                 ?(i) Or \[g'=\frac{GM}{{{(R+h)}^{2}}}\]                    ?(ii) Equating eqns. (i) and (ii), we get \[9{{R}^{2}}={{(R+h)}^{2}}\] Or \[3R=R+h\] or \[h=3R-R=2R\]


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