A heavy cylindrical shaft (pile) of mass $$M$$ is driven vertically through a distance $$s$$ into the ground by the blow of a pile-driver of mass $$m$$. The pile driver drops vertically through a distance $$h$$ onto the head of the pile. The average resistance of the ground is

A

$$g\left[\frac{m^2}{M}\frac{h}{s} + 2m\right]$$

B

$$g\left[\frac{m^2}{(m + M)}\frac{h}{s} + (m + M)\right]$$

C

$$g\left[\frac{M^2}{m}\frac{h}{s} + (m + M)\right]$$

D

$$g\left[\frac{m^2}{(m + M)}\frac{h}{s} + 2(m + M)\right]$$