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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Self Evaluation Test - Gravitation

  • question_answer
    An artificial satellite is first taken to a height equal to half the radius of earth. Assume that it is at rest on the earth's surface initially and that it is at rest at this height. Let \[{{E}_{1}}\]be the energy required. It is then given the appropriate orbital speed such that it goes in a circular orbit at that height. Let E be the energy required. The ratio \[\frac{{{E}_{1}}}{{{E}_{2}}}\] is

    A) 4:1

    B) 3:1  

    C) 1:1

    D) 1:2

    Correct Answer: C

    Solution :

    [c] \[{{E}_{1}}=-\frac{G{{M}_{e}}m}{{{\operatorname{R}}_{e}}+\frac{{{\operatorname{R}}_{e}}}{2}}\left( -\frac{G{{M}_{e}}m}{{{\operatorname{R}}_{e}}} \right)=\frac{G{{M}_{e}}m}{3{{\operatorname{R}}_{e}}}\] \[{{E}_{2}}=\frac{1}{2}m{{v}_{0}}^{2}=\frac{1}{2}m.\frac{G{{M}_{e}}}{{{\operatorname{R}}_{e}}+\frac{{{\operatorname{R}}_{e}}}{2}}=\frac{G{{M}_{e}}m}{3{{\operatorname{R}}_{e}}}\] \[\therefore \frac{{{E}_{1}}}{{{E}_{2}}}=1:1\]


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