\({r}\) \({V(r) =k\left( \dfrac{r_{0}-r}{c}\right) r^{4}}\)
\(\dfrac{r_{0}}{2}\) \(k\left( \dfrac{r_{0}-\dfrac{r_{0}}{2}}{c}\right) \left( \dfrac{r_{0}}{2}\right) ^{\!\!4}=\dfrac{k\,r_{0}^{5}}{32c}\)
\(\dfrac{4r_{0}}{5}\) \(k\left( \dfrac{r_{0}-\dfrac{4r_{0}}{5}}{c}\right) \left( \dfrac{4r_{0}}{5}\right) ^{\!\!4}=\dfrac{k}{c}\cdot \dfrac{ 4^{4}\,r_{0}^{5}}{5^{5}}=\dfrac{256\,k\,r_{0}^{5}}{3125c}\)
\(r_{0}\) \(0\)