Chapter 2, Problem 2.15P

Interpretation Introduction

Interpretation:

To derive a formula for ${\text{ρ}}_{\text{f}}$ in terms of ${\text{ρ}}_{\text{s}}$, R and h/H.

Concept introduction:

According to Archimedes’ principle, both the masses that is the mass of fluid displaced by the body and mass of the floating body is similar to each other.

To obtain mass of the fluid displaced by the object:

1. Total volume of the right-circular cone is:

$V_{\text{cone}}=\frac{\pi R^{2}h}{3}$

2. Volume of the cone that floats on water is

$V^{\text{'}}=\frac{\pi r^{2}h}{3}$

where, h is height of the cone that is not submerged and r is the radius at the surface of the water.