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JEE Main & Advanced Sample Paper JEE Main Sample Paper-1

  • question_answer
    The minimum kinetic energy needed to project a body of mass m from the earth's surface to infinity is [g is acceleration due to gravity at earth's surface]

    A)  \[\frac{1}{4}\]mgR                         

    B)  \[\frac{1}{2}\]mgR

    C)  mgR                                     

    D)  2 mgR

    Correct Answer: C

    Solution :

    For minimum KE, the velocity at infinite should be zero. Apply energy conservation \[\frac{m{{v}^{2}}}{2}-\frac{GMm}{R}=0\] \[\Rightarrow \] \[\frac{m{{v}^{2}}}{2}-\frac{GMm}{R}\] \[\Rightarrow \] \[KE=\frac{GMm}{R}\] \[=\frac{GMm}{{{R}^{2}}}\times R=mgR\]


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