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9th Class Science Gravitation and Floatation Question Bank Gravitation Summative Objective Problems

  • question_answer
    Assume that earth is a spherical planet of uniform density\[\rho ,\]radius \[{{R}_{e}},\]mass\[{{M}_{e}}\]and acceleration due to gravity g. Then the gravitational constant G can be written as

    A)  \[\frac{3}{4\pi \rho {{R}_{e}}}\]               

    B)  \[\frac{gR_{e}^{2}}{{{M}_{e}}}\]

    C)  \[\frac{3g}{4\pi \rho R_{e}^{2}}\]                           

    D)  \[\frac{12\rho g}{4\pi {{R}_{e}}}\]

    Correct Answer: A

    Solution :

      \[g=\frac{GM}{{{R}^{2}}},\,\,e=\frac{M}{V}=\frac{M}{\frac{4}{3}\pi R_{e}^{2}},\,\,g=\frac{4}{3}\pi GeR\] \[\Rightarrow G=\frac{gR_{e}^{2}}{{{M}_{e}}},\,G=\frac{3g}{4\pi \rho {{R}_{e}}}\]          


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