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CMC Medical CMC-Medical VELLORE Solved Paper-2010

  • question_answer
    How much work per kilogram need to be done to shift a 1 kg mass from the surface of the earth to the infinity? (Take acceleration due to gravity = g, and radius of the earth = R)

    A)  \[\frac{g}{R}\]                                 

    B)  Rg

    C)  \[g{{R}^{2}}\]                                   

    D)  \[\frac{g}{{{R}^{2}}}\]

    E)  None of these

    Correct Answer: B

    Solution :

                    Gravitational potential from the surface of earth to gravitational potential at\[\infty =0\] Potential difference\[=-\,0-\left( -\frac{GM}{R} \right)\] \[\Delta V=\frac{GM}{R}\] Work done in shifting a body of mass m kg from the surface of earth to infinity. \[W=m\Delta V\]     \[=\frac{GMm}{R}\] \[\therefore \]Work done per kg\[=\frac{GM}{R}=gR\]


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