Question

How far below the interface between the two liquids is the bottom of the block

Answer 1

Option 1

Step-by-step explanation

Parameters given:

Density of oil, ρo = 923kg/m^3

Density of water, ρw = 997 kg/m^3

Density of block, ρb = 966 kg/m^3

Height of block, h = 4.46 cm = 0.0446 m

To find the depth of the bottom of the block below the interface, since they are in equilibrium, we have to apply the equilibrium equation:

`\rho_bgh-\rho_og(h-x)-\rho_wgx=0`

where x = distance of the bottom of the block below the interface

g = acceleration due to gravity

We have to solve for x by substituting the given values into the equation and simplifying:

`\begin{gathered} 966\cdot g\cdot0.0446-923\cdot g\cdot(0.0446-x)-997\cdot g\cdot x=0 \\ \Rightarrow43.0836g-923g(0.0446-x)-997gx=0 \end{gathered}`

Dividing through by g:

`\begin{gathered} 43.0836-923(0.0446-x)-997x=0 \\ 43.0836-41.1658+923x-997x=0 \\ 43.0836-41.1658=997x-923x \\ \Rightarrow1.9178=74x \\ \Rightarrow x=(1.9178)/(74) \\ x=0.02591 \end{gathered}`

That is the distance.

The closest option is option 1.