Find out the fundamental units involved in the given derived units: i) newton (N), ii) watt (W), iii) joule (J), iv) pascal (Pa)
Solution
To find the fundamental units involved in the given derived units, we first write their corresponding fundamental physical quantities and definitions.
i) newton (N)
Newton is the unit of Force. And, $$\rm Force = mass \times acceleration$$
$$\rm N = kg \cdot ms^{-2}$$
Therefore, newton involves three fundamental units: kilogram (kg), meter (m), and second (s).
ii) watt (W)
Watt is the unit of Power. And, $$\rm Power = Force \times velocity$$
$$\rm W = kgms^{-2} \cdot ms^{-1}$$
Therefore, watt involves three fundamental units: kilogram (kg), meter (m), and second (s).
iii) joule (J)
Joule is the unit of Work. And, $$\rm Work = Force \times distance$$
$$\rm J = kgms^{-2} \cdot m$$
Therefore, joule involves three fundamental units: kilogram (kg), meter (m), and second (s).
iv) pascal (Pa)
Pascal is the unit of Pressure. And $$\rm Pressure = \frac{Force}{Area}$$
$$\rm Pa = \frac{kgms^{-2}}{m^2}$$
Therefore, pascal involves three fundamental units: kilogram (kg), meter (m), and second (s).