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

  • question_answer
    An asteroid of mass m is approaching earth initially at a distance of\[10{{\operatorname{R}}_{e}}\], with speed\[{{v}_{i}}\]. It hits the earth with a speed \[{{v}_{f}}({{\operatorname{R}}_{e}}\,\,and\,\,{{M}_{e}}\], are radius and mass of earth), then    

    A)  \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{M}_{e}}R}\left( 1-\frac{1}{10} \right)\]                      

    B) \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1+\frac{1}{10} \right)\]

    C) \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\]            

    D) \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\]

    Correct Answer: C

    Solution :

    [c] \[-\frac{G{{M}_{e}}m}{10{{\operatorname{R}}_{e}}}+\frac{1}{2}m{{v}_{i}}^{2}=-\frac{G{{M}_{e}}m}{{{\operatorname{R}}_{e}}}+\frac{1}{2}m{{v}_{f}}^{2}\] \[\therefore {{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\].


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