Beyond fluids, Archimedes’ principle has proven useful in geology when applied to solids o...

Beyond fluids, Archimedes’ principle has proven useful in geology when applied to solids on the earth’s crust. Figure P1.25 depicts one such case where a lighter conical granite mountain “floats on” a denser basalt layer at the earth’s surface. Note that the part of the cone below the surface is formally referred to as a frustum. Develop a steady-state force balance for this case in terms of the following parameters: basalt’s density (ρ_b), granite’s density (ρ_g), the cone’s bottom radius (r), and the height above (h₁) and below (h₂) the earth’s surface.

Figure P1.25: