Chapter 6, Problem 89A

Interpretation Introduction

Interpretation:

To determine whether the cube of plastic will float or sink in water.

Concept Introduction :

Relation between mass, volume, and density is as shown:

  $\text{density}=\frac{\text{mass}}{\text{volume}}$

Answer to Problem 89A

Float on the water surface

Explanation of Solution

Mass of cube is $1.70\text{ g}$

Side of the plastic cube is $1.20\times {10}^{-5}\text{ km}$

Convert side of the cube in cm as shown:

  $\begin{array}{c}1.20\times {10}^{-5}\text{ km}=1.20\times {10}^{-5}\text{ km}\times \frac{1\text{ cm}}{1\times {10}^5\text{ km}}\\ =1.20\text{ cm}\end{array}$

Calculate volume of cube as,

  $\begin{array}{c}\text{volume of cube}={\left(1.20\text{ cm}\right)}^3\\ =\text{1}{\text{.728 cm}}^{\text{3}}\end{array}$

Now, calculate the density

  $\begin{array}{c}\text{density of cube}=\frac{1.70\text{ g}}{1.728{\text{ cm}}^{\text{3}}}\\ =\text{0}\text{.98 }\text{g}/{\text{cm}}^{\text{3}}\end{array}$

Density of water is $\text{1 }\text{g}/{\text{cm}}^{\text{3}}$ .

As the density of plastic cubes is less than the density of water, thus, the plastic cube will float on the water surface.