9th Class Science Gravitation and Floatation Question Bank Gravitation

  • question_answer
    An artificial satellite of mass 200 kg revolves around the earth in an orbit of average radius 667 km. Its total energy in the orbit is (Mass of the earth = \[6.0\times {{10}^{24}}kg\]  and\[~\text{G }=\text{ 6}.\text{67 }\times \text{1}{{0}^{-\text{11}}}\text{ N}-{{m}^{2}}\text{/k}{{\text{g}}^{\text{2}}})\]

    A) \[\text{6}.\text{6 }\times \text{ 1}{{0}^{9}}\text{ joule}\] 

    B)         \[-\text{ 6}.\text{6 }\times \text{ 1}{{0}^{\text{9}}}\text{ joule}\]  

    C) \[\text{6}.\text{6 }\times \text{ 1}{{0}^{-\text{9}}}\text{ joule}\]

    D)        \[-\text{ 6}.\text{6 }\times \text{ 1}{{0}^{-\text{9}}}\text{ joule}\]

    Correct Answer: B

    Solution :

                    \[K.E.=\frac{G{{M}_{e}}m}{2r}\] \[\therefore \]          \[=\frac{(6.67\times {{10}^{-11}})(6.0\times {{10}^{24}})(200)}{2\times (6670\times {{10}^{3}})}\]                         \[=6.0\times {{10}^{9}}\] joule. Gravitation potential energy,                 \[U=\frac{G{{M}_{e}}m}{r}=-12.0\times {{10}^{9}}\]joule \[\therefore \]Total energy, \[T=U+K=\mathbf{-6}\mathbf{.6\times 1}{{\mathbf{0}}^{\mathbf{9}}}\]joule.


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