Chapter 1, Problem 26P

Beyond fluids, Archimedes' principle has proven useful in geology when applied to solids on the earth's crust. Figure P1.26 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 $\left({\rho }_b\right)$, granite's density $\left({\rho }_g\right)$, the cone's bottom radius $\left(r\right)$, and the height above $\left(h_1\right)$ and below $\left(h_2\right)$ the earth's surface

FIGURE P1.26