Question

Rank in order, from largest to smallest, the densities of blocks a, b, and c in FIGURE Q14.6. Explain.

Short answer

Density in descending order is ρ_a> ρ_c > ρ_b

Step-by-step solution

Given information

Given figure shows three blocks floating in liquid.

Explanation

We know that buoyant force acting on a mass floating in a liquid depends on density or object, submerged volume of object and gravity.

$F_{buoyant}=V_s\rho g$

Lets assume three blocks are floating have Volume V_a, V_b and V_cand density ρ_a, ρ_band ρ_c

Then

$$\begin{gathered} V_{s_a}\rho g=V_a{\rho }_{a}g\Rightarrow {\rho }_a=\left(\frac{V_{s_a}}{V_a}\right)\rho \\ {V}_{s_b}\rho g=V_b{\rho }_{b}g\Rightarrow {\rho }_b=\left(\frac{V_{s_b}}{V_b}\right)\rho \\ {V}_{sc}\rho g=V_c{\rho }_{c}g\Rightarrow {\rho }_c=\left(\frac{V_{s_{-}c}}{V_c}\right)\rho \end{gathered}$$

So density depends on the ratio of submerged volume to the total volume.

From the figure we can see that

$\left(\frac{V_{S_{-}a}}{V_a}\right)>\left(\frac{V_{S_{-}c}}{V_c}\right)>\left(\frac{V_{S_{-}b}}{V_b}\right)$

This means the densities are in the order

ρ_a> ρ_c > ρ_b