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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

  • question_answer
    If the gravitational force had varied as \[{{r}^{-5/2}}\] instead of \[{{r}^{-2}}\], the potential energy of a particle at a distance \[r\]from the centre of the earth would be proportional to

    A)  \[{{r}^{-1}}\]                                 

    B)  \[{{r}^{-2}}\]

    C)  \[{{r}^{-3/2}}\]                              

    D)  \[{{r}^{-5/2}}\]

    Correct Answer: C

    Solution :

     Potential energy at a distance r from the centre of earth is, \[U=-\,\int_{\infty }^{r}{-F\,dr}\] where, F is the gravitational force \[F=\frac{GMm}{{{r}^{5/2}}}\]  \[U=\int_{\infty }^{r}{\frac{GMm}{{{r}^{5/2}}}}\,dr=-\frac{2}{3}\,\frac{GMm}{{{r}^{3/2}}}\] i.e.,      \[U\propto {{r}^{-3/2}}\]


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