Chapter U1.5, Problem 7E

Interpretation Introduction

(a)

Interpretation:

Density of a marble must be found out which has mass and volume 18.5 g and 6.45 cm³ respectively.

Concept introduction:

Density of a substance is the ratio of mass to the volume.

Thus,

$d=\frac{m}{V}$

Here, m is mass and V is volume.

Answer to Problem 7E

Density of the marble is 2.87 g/cm³

Explanation of Solution

Mass of the marble is give as 18.5 g. Volume is given as 6.45 cm³.

The density can be calculated as follows:

$d=\frac{m}{V}$

Putting the values,

$d=\frac{18.5\text{ g}}{6.45{\text{ cm}}^{\text{3}}}=2.87{\text{ g/cm}}^{\text{3}}$

Interpretation Introduction

(b)

Interpretation:

Mass and volume of six marbles must be found out where each marble has mass and volume of 18.5 g and 6.45 cm³ respectively.

Concept introduction:

Mass and volume are additive in nature.

Answer to Problem 7E

Mass of six marbles is 111g and volume of six marbles is 38.7 cm³.

Explanation of Solution

One marble has mass of 18.5 g.

So, six marbles will have mass of $6\times 18.5g=11\text{1 g}$

Similarly, volume of six marbles $=6\times 6.45{\text{ cm}}^{\text{3}}=\text{38}{\text{.7 cm}}^{\text{3}}$

Interpretation Introduction

(c)

Interpretation:

The density of one marble needs to be compared with density of six marbles.

Concept introduction:

Density is same for all similar objects. It is not an additive property.

Answer to Problem 7E

Density of one marble is same to the density of six marbles.

Explanation of Solution

Density is not an additive property. Thus, density will not change when number of marble is changed from one to six. So, all the similar marbles will have same density, that is, 2.87 g/cm³.