The mass density of a spherical body is given by ρ(r) = (k)/(r) for...

 For Inside point $\left(r \le R\right)$

$g = E = \dfrac{G}{{r}^{2}}\mathop{∫}_{0}^{r}\left(4\pi{r}^{2}dr\right)\left(\dfrac{K}{r}\right)$
$\dfrac{GK}{{r}^{2}} \times \dfrac{4\pi{r}^{2}}{2} = 2\piGK = constant$

For outside point \left(r > R\right)$<br/><br/>$E = g = \dfrac{GM}{{r}^{2}} = \dfrac{G}{{r}^{2}} \mathop{∫}_{0}^{R} ( 4\pi{r}^{2} d{r}^{′} )( \dfrac{K}{{r}^{′}} ) = \dfrac{4\piKG}{{r}^{2}} {[ \dfrac{{{r}^{′}}^{2}}{2} ]}_{0}^{R}$<br/><br/>$E = g = \dfrac{2\piKG}{{r}^{2}}{R}^{2}$<br/><br/>$E ∝ \dfrac{1}{{r}^{2}}