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JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    The change in the gravitational potential energy when a body of mass \[m\] is raised to a height \[nR\] above the surface of the earth is (here, \[R\] is the radius of the earth)

    A) \[\left( \frac{n}{n+1} \right)mgR\]                          

    B) \[\left( \frac{n}{n-1} \right)mgR\]

    C) \[nmgR\]                            

    D) \[\frac{mgR}{n}\]

    Correct Answer: A

    Solution :

    Gravitational potential energy                 \[{{U}_{e}}=\frac{GMm}{R}\]                 \[{{U}_{h}}=\frac{GMm}{(R+nR)}=-\frac{GMm}{R(n+1)}\]                 \[\Delta U={{U}_{h}}-{{U}_{e}}\]                 \[=\frac{GMm}{R}\left[ 1-\frac{1}{(n+1)} \right]\]                 \[=\frac{n}{(n+1)}\left[ \frac{GMm}{R} \right]\]                 \[=\frac{n}{(n+1)}mgR\]


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