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CMC Medical CMC-Medical VELLORE Solved Paper-2015

  • question_answer
    A body of mass m is released from a height equal to the radius R of the earth. What will be the velocity of the body when it strikes the surface of the earth?

    A)  \[\sqrt{2}gR\]                  

    B)  \[\sqrt{gR}\]

    C)  \[\frac{gR}{\sqrt{2}}\]                                  

    D)  \[\sqrt{3gR}\]

    E)  \[\frac{\sqrt{gR}}{3}\]

    Correct Answer: B

    Solution :

                    From work-energy theorem, \[\frac{1}{2}m{{v}^{2}}=-\,GMm\left[ \frac{1}{2R}-\frac{1}{R} \right]\] \[\Rightarrow \]               \[\frac{1}{2}m{{v}^{2}}=\frac{-\,GMm}{2R}\] \[\Rightarrow \]               \[v=\sqrt{gR}\] \[\left( \because g=\frac{GM}{{{R}^{2}}} \right)\]


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