Gravitational Potential for Different Bodies
Category : JEE Main & Advanced
(1) Potential due to uniform ring
| At a point on its axis | At the centre |
| \[V=-\frac{GM}{\sqrt{{{a}^{2}}+{{r}^{2}}}}\] | \[{{T}^{2}}\propto {{r}^{3}}\] |
(2) Potential due to spherical shell
| Outside the surface r > R | On the surface r = R | Inside the surface r < R |
| \[V=\frac{-GM}{r}\] | \[V=\frac{-GM}{R}\] | \[V=\frac{-GM}{R}\] |
(3) Potential due to uniform solid sphere
| Outside the surface r > R | On the surface r = R | Inside the surface r < R |
| \[{{T}^{2}}=\frac{4{{\pi }^{2}}}{GM}{{r}^{3}}\] | \[{{V}_{surface}}=\frac{-GM}{R}\] | \[T=2\pi \sqrt{\frac{{{r}^{3}}}{GM}}\] at the centre (r = 0) \[{{V}_{centre}}=\frac{-3}{2}\frac{GM}{R}\] (max.) Vcentre = \[\frac{3}{2}{{V}_{surface}}\] |
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