>>508328714
Assume
> penetrator velocity < speed of sound in rock
> Penetrator coheisive forces at this velocity are relatively much greater than the impacted material (ignore pic related)

The aproximation reduces to aconservation of momentum problem. Mass displaced = Mass of displacing object. Increasing the diameter of the object increases both the mass of displaced matter but also the mass of the displacor in direct proportion. The problem then reduces to the relative density of the material displaced, and the mass of a uniformly dense object is proportional to its length.