Explanation

(d) $Centripetal\ force\ F = - \frac{k}{r^{2}}$
$\frac{{mv}^{2}}{r} = \frac{k}{r^{2}} \Longrightarrow {mv}^{2} = \frac{k}{r}$
$Kinetic\ energy = \frac{1}{2}{mv}^{2} = \frac{k}{2r}$
Since the centripetal force is a conservative force, and for a conservative force,
$F = \frac{dU}{dr} \Longrightarrow U = - \int_{}^{}{F \bullet dr}$
$U = \int_{}^{}{\frac{k}{r^{2}}dr = - \frac{k}{r}}$
$Toatal\ energy = K + U = \frac{k}{2r} - \frac{k}{r} = - \frac{k}{2r}$