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

  • question_answer
    If g is acceleration due to gravity on the surface of the earth having radius R, the height above the surface of earth at which the acceleration due to g gravity reducer to\[\frac{g}{2}\]is

    A)  \[\frac{R}{2}\]                                 

    B)  \[(\sqrt{2}-1)R\]

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

    D)  \[\frac{121R}{100}\]

    Correct Answer: B

    Solution :

       \[{{g}_{1}}\frac{g{{R}^{2}}}{{{(R+h)}^{2}}}\Rightarrow \frac{g}{2}=\frac{g{{R}^{2}}}{{{(R+h)}^{2}}}\] \[\Rightarrow \frac{1}{\sqrt{2}}=\frac{R}{R+h}\Rightarrow R+h=\sqrt{2}R\,\,or\,h=(\sqrt{2}-1)R\]


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