Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S29 / 2 / 3

In a gravity-dominated excavation model, displaced mass scales as $\rho D^3$ and lifting it through a distance of order $D$ costs order $\rho g{D}^4$. If a comparable fraction of impact energy supplies this work across similar impacts, $\boxed{D\propto E_{\mathrm{impact}}^{1/4}}$. This is a scaling justification, not a universal crater law: strength-dominated small craters or varying coupling efficiencies can have different exponents.