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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2004

  • question_answer
    How much energy will be necessary for making a body of 500 kg escape from the earth? \[\text{ }\!\![\!\!\text{ g}\,\text{=}\,\text{9}\text{.8}\,\text{m}{{\text{s}}^{2}},\] radius of the earth \[\text{6}\text{.4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{6}}}\text{m }\!\!]\!\!\text{ }\]

    A)  About \[9.8\times {{10}^{6}}J\]

    B)  About \[6.4\times {{10}^{8}}J\]

    C)  About \[3.1\times {{10}^{10}}J\]             

    D)  About \[27.4\times {{10}^{12}}J\]

    Correct Answer: C

    Solution :

    Escape velocity \[{{v}_{e}}=\sqrt{2gR}\] Kinetic energy of the body required to escape                 \[KE=\frac{1}{2}mv_{e}^{2}\] or            \[KE=\frac{1}{2}m(2gR)\] or            \[KE=mgR\] or            \[KE=500\times 9.8\times 6.4\times {{10}^{6}}\] \[\Rightarrow \]               \[KE=3.1\times {{10}^{10}}J\]


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