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

  • question_answer
    A shell is fired vertically from the earth with speed \[\frac{{{V}_{esc}}}{N},\] where Nis some number greater than one and V is escape speed for the earth. Neglecting the nation of the earth and air resistance, the maximum altitude attained by the shell will be is radius of the earth)                      

    A) \[\frac{{{N}^{2}}{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\]

    B) \[\frac{N{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\]

    C) \[\frac{{{\operatorname{R}}_{E}}}{{{N}^{2}}-1}\]

    D) \[\frac{{{\operatorname{R}}_{E}}}{{{N}^{2}}}\]

    Correct Answer: C

    Solution :

    [c] By conservation of energy \[-\frac{GMm}{{{R}_{E}}}\text{+}\frac{1}{2}\frac{m}{{{N}^{2}}}\frac{GM}{2{{R}_{E}}}\text{=-}\frac{GMm}{H}\] \[\Rightarrow H=\frac{{{N}^{2}}{{R}_{E}}}{{{N}^{2}}-1}\] Altitude \[=H-R=\frac{{{R}_{E}}}{{{N}^{2}}-1}\]


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