Question

Isostasy is an important concept in the geosciences that is related to density. The concept of isostasy explains why continental crust sits so much higher than oceanic crust. It involves properties of an object like height and density. It also explains why only a portion of an iceberg is visible above water. The equation for calculating the height of an object above the "fluid" in which it is floating is:

Answer 1

ANSWER

Option A:

$A.\text{ }(1-\frac{H_{above}}{H_{total}})(\rho_{flu\imaginaryI d})$

EXPLANATION

We have to solve the formula for ρ_object. To do so, first, divide both sides by H_total,

$\begin{gathered} \frac{H_{total}*(1-\frac{\rho_{objet}}{\rho_{fluid}})}{H_{total}}=\frac{H_{above}}{H_{total}} \\ \\ \left(1-\frac{\rho_{object}}{\rho_{fluid}}\right)=\frac{H_{above}}{H_{total}} \end{gathered}$

Then, subtract 1 from both sides,

$\begin{gathered} 1-1-\frac{\rho_{object}}{\rho_{fluid}}=\frac{H_{above}}{H_{total}}-1 \\ \\ \begin{equation*} -\frac{\rho_{object}}{\rho_{fluid}}=\frac{H_{above}}{H_{total}}-1 \end{equation*} \end{gathered}$

And then, multiply both sides by -ρ_fluid,

$\begin{gathered} -\frac{\rho_{object}}{\rho_{fluid}}\cdot(-\rho_{fluid})=\left(\frac{H_{above}}{H_{total}}-1\right)\cdot(-\rho_{fluid}) \\ \\ \rho_{object}=\left(1-\frac{H_{above}}{H_{total}}\right)\cdot(\rho_{fluid}) \end{gathered}$

Hence, the formula for ρ_object is,

$\rho_{object}=(1-\frac{H_{above}}{H_{total}})(\rho_{flu\imaginaryI d})$