Which of the following is an si derived unit? joule (j) kilogram (kg) meter (m) second (s)
The Correct Answer and Explanation is :
The correct answer is joule (J).
The International System of Units (SI) consists of base units and derived units. Base units are the fundamental units that describe basic physical quantities, while derived units are formed from these base units through multiplication or division. In this context, the joule is an SI derived unit used to measure energy, work, or heat.
To understand why the joule is a derived unit, we can break it down into its base components. A joule is defined as the amount of energy transferred when a force of one newton is applied over a distance of one meter. Thus, the joule can be expressed in terms of other SI base units:
[
1 \, \text{J} = 1 \, \text{N} \cdot 1 \, \text{m}
]
Where:
- Newton (N) is the unit of force, defined as (1 \, \text{kg} \cdot \text{m/s}^2).
- Meter (m) is the unit of length.
Substituting the definition of the newton into the equation for joules, we get:
[
1 \, \text{J} = 1 \, \text{(kg} \cdot \text{m/s}^2) \cdot 1 \, \text{m} = 1 \, \text{kg} \cdot \text{m}^2/\text{s}^2
]
This relationship illustrates how the joule is derived from the base units of kilogram (kg), meter (m), and second (s).
In contrast, the other options listed—kilogram, meter, and second—are all base units in the SI system. The kilogram measures mass, the meter measures length, and the second measures time. Together, these base units serve as the foundation for the derived units like joules, highlighting the interconnectedness of physical measurements. Understanding the distinction between base and derived units is essential for interpreting scientific data accurately and for engaging in various fields of study, including physics and engineering.