A central force is $\mathbf F=-k\hat{\mathbf r}/r^3$, where $\hat{\mathbf r}$ points away from the centre. Taking zero potential at infinity, the potential energy is
For a central potential, $F_r=-dU/dr$. Thus $dU/dr=k/r^3$, and integrating gives $U=-k/(2r^2)+C$. The condition $U(\infty)=0$ fixes C = 0. Differentiating the result confirms the inward force, so D.
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