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AMU Medical AMU Solved Paper-2012

  • question_answer
    A particle in a certain conservative force field has a potential energy given by \[U=20\,\,xy/z\]. The force exerted on it is

    A)  \[(20\,y/z)\,i+(20x/z)\,j+(20\,xy/{{z}^{2}})\,k\]

    B)  \[-(20\,y/z)\,i-(20x/z)\,j+(20\,xy/{{z}^{2}})\,k\]

    C)  \[-(20\,y/z)\,i+(20x/z)\,j-(20\,xy/{{z}^{2}})\,k\]

    D)  \[(20\,y/z)\,i+(20x/z)\,j-(20\,xy/{{z}^{2}})\,k\]

    Correct Answer: D

    Solution :

                     Potential energy                 \[U=20xy/z\]                 \[F=\frac{dU}{dx}=\frac{d{{U}_{x}}}{dx}+\frac{d{{U}_{y}}}{dy}+\frac{d{{U}_{z}}}{dz}\]                 \[=\frac{20y}{z}\,i+\frac{20x}{z}j-\frac{20xy}{{{z}^{2}}}k\]           


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