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

  • question_answer
    A spherical planet in the space having a mass 'M' and diameter D. A particle of mass m falls freely near the surface of the planet with an acceleration due to gravity which is equal to

    A)  \[\text{GM}/{{\text{D}}^{\text{2}}}\]                  

    B)  \[\text{GMm}/{{\text{D}}^{\text{2}}}\]

    C)  \[\text{4 GM}/{{\text{D}}^{\text{2}}}\]               

    D)  \[\text{4m GM}/{{\text{D}}^{\text{2}}}\]

    Correct Answer: C

    Solution :

      \[g=\frac{4}{3}\pi GeR\]                                               ????.(1) \[e=\frac{M}{V}=\frac{M}{\frac{4}{3}\pi {{\left( \frac{D}{2} \right)}^{3}}}=\frac{8M}{\frac{4}{3}\pi .{{D}^{3}}}\]                ??..(2) \[\therefore \,\,g=\frac{4}{3}\pi G.\,\,\frac{8M}{\frac{4}{3}\pi {{D}^{3}}}.\,\,\frac{D}{2}=\frac{4GM}{{{D}^{2}}}\]


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