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 = gE = \dfrac{GM}{{r}^{2}}E = \dfrac{G}{{r}^{2}}\mathop{∫}_{0}^{R}( 4\pi{r}^{2}d{r}^{'} )( \dfrac{K}{{r}^{'}} )E = \dfrac{4\piKG}{{r}^{2}}{[ \dfrac{{{r}^{'}}^{2}}{2} ]}_{0}^{R}$<br /><br />$E = \dfrac{2\piKG}{{r}^{2}}{R}^{2}$<br /><br />$E ∝ \dfrac{1}{{r}^{2}}.