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., \[U\propto {{r}^{-3/2}}\]You need to login to perform this action.
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