Chapter 1, Problem 65A

(a)

To determine

To Write: The metric unit of density.

Answer to Problem 65A

  ${\text{kg/m}}^{\text{3}}$

Explanation of Solution

Given:

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

Formula Used:

SI unit of mass is kilogram (kg).

SI unit of length is meter (m).

Calculations:

Unit of volume can be derived from the base unit meter. Unit of volume is cubic meter $\left({\text{m}}^{\text{3}}\right)$ .

The metric unit of density would be:

  $\text{Density=}\frac{\text{mass}\left(\text{kg}\right)}{\text{volume}\left({\text{m}}^{\text{3}}\right)}$

The metric unit of density is: ${\text{kg/m}}^{\text{3}}$

Conclusion:

Thus, the metric unit of density is ${\text{kg/m}}^{\text{3}}$ .

(b)

To determine

Whether the unit for density is base unit or derived unit.

Answer to Problem 65A

Derived unit

Explanation of Solution

Introduction:

SI system has seven base units which further help to define 22 derived units. The SI unit of mass, time, length, thermodynamic temperature, amount of substance, electric current and luminous intensity are the base units. A derived unit is product of two or more base units.

SI unit of mass is kilogram (kg). SI unit of length is meter (m). Unit of volume can be derived from the base unit meter. Unit of volume is cubic meter $\left({\text{m}}^{\text{3}}\right)$ .

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

The metric unit of density is: ${\text{kg/m}}^{\text{3}}$

Conclusion:

Thus, it can be concluded that the metric unit of density is a derived unit.