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9th Class Science Gravitation and Floatation Question Bank Gravitation

  • question_answer
    Mass of the earth is 81 times the mass of the moon and distance between the earth and moon is 60 times the radius of the earth. If R is radius of the earth, then distance between the moon and the point on the line joining the moon and earth where the gravitational force becomes zero is

    A)  30R

    B)  15R

    C)  6R  

    D)  5R

    Correct Answer: C

    Solution :

     Let \[m\] be the mass at a distance \[x\] from the centre of the moon where gravitation force is zero. \[\therefore \]  \[\frac{G{{M}_{e}}m}{{{(60R-x)}^{2}}}=\frac{G{{M}_{moon}}m}{{{x}^{2}}}\] or            \[\frac{81}{{{(60R-x)}^{2}}}=\frac{1}{{{x}^{2}}}\]               \[\text{or}\]\[\frac{9}{60-x}=\frac{1}{x}\] or            \[x=6R\]


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