Chapter 1.2, Problem 9R

To determine

To explain: Density is a derived unit.

Explanation of Solution

Introduction:

Derived unit means a quantity which cannot be directly measured using any device or instrument.The derived units are either dimensionless or can be expressed as a product of one or more units. Density is stated as a derived unit because it is basically defined or expressed in terms of other units.

The density of an object is given by the ratio of the mass of the object and its volume and can be expressed as,

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

It can be noted that the density of an object does not depend on the quantity of mass present. This is so because as the mass of an object increases, the volume also increases and the ratio of the two quantities always remains same for a given object. Thus, density is an intensive quantity. The SI unit of density is kilogram per cubic meter (kg/m³). The unit of density is thus derived from mass and volume of an object.

Conclusion:

Hence, density is a derived unit.