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

  • question_answer
    Find the ratio of weights of a body at heights \[{}^{R}/{}_{2}\] and \[{}^{R}/{}_{3}\]from the surface of the earth (where R is the radius of the earth)

    A)  \[\frac{3}{2}\]                                  

    B)  \[\frac{2}{3}\]

    C)  \[\frac{64}{81}\]                             

    D)  \[\frac{1}{2}\]

    Correct Answer: C

    Solution :

       \[\frac{{{W}_{1}}}{{{W}_{2}}}=\frac{{{g}_{1}}}{{{g}_{2}}}\] \[{{g}_{1}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{2} \right)}^{2}}};\,\,{{g}_{2}}=\frac{g{{R}^{2}}}{{{\left( R+\frac{R}{3} \right)}^{2}}}\] \[\therefore \frac{{{W}_{1}}}{{{W}_{2}}}=\frac{{{\left( R+\frac{R}{3} \right)}^{2}}}{{{\left( R+\frac{R}{3} \right)}^{2}}}=\frac{\frac{16}{9}}{\frac{9}{4}}=\frac{64}{81}\]     


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