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

  • question_answer
    If the force of gravitation between the earth and a body of mass M on its surface be\[\text{9}\times \text{1}0\text{7 N,}\] what would be the value of M? Mass of the earth\[=\text{6}\times \text{1}0\text{24}\,\text{kg}\].

    A)              \[\text{9}.\text{2}\times \text{1}{{0}^{\text{3}}}\text{ kg}\]                     

    B)  \[\text{9}.\text{2}\times \text{1}{{0}^{5}}\text{ kg}\]

    C)  \[\text{9}.\text{2}\times \text{1}{{0}^{\text{6}}}\text{ kg}\]        

    D)  \[\text{9}.\text{2}\times \text{1}{{0}^{\text{9}}}\text{ kg}\]

    Correct Answer: C

    Solution :

       \[F=9\times {{10}^{7}}N\] Mass of the earth, \[{{m}_{1}}=6\times {{10}^{24}}kg\] Mass of the body, \[{{m}_{2}}=M\] Radius of the earth, \[r=6.4\times {{10}^{6}}m\] \[G=6.67\times {{10}^{-11}}N{{m}^{2}}k{{g}^{-2}}\] \[F=G=\frac{{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] \[9\times {{10}^{7}}=\frac{6.67\times {{10}^{-11}}\times M\times 6\times {{10}^{24}}}{{{(6.4\times {{10}^{6}})}^{2}}}\,or\] \[M=\frac{6\times 6.4\times 6.4\times {{10}^{6}}}{6.67\times 6}kg=9.2\times {{10}^{6}}kg\]      


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