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Difficulty: MediumFundamental and Derived Units

Match each derived SI unit listed on the left with its corresponding fundamental (base) SI unit representation on the right.

  • Joule (J\text{J})kg⋅m2⋅s−2\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}
  • Pascal (Pa\text{Pa})kg⋅m−1⋅s−2\text{kg}\cdot\text{m}^{-1}\cdot\text{s}^{-2}
  • Watt (W\text{W})kg⋅m2⋅s−3\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}
  • Newton (N\text{N})kg⋅m⋅s−2\text{kg}\cdot\text{m}\cdot\text{s}^{-2}

Answer

Joule (J\text{J}) matches kg⋅m2⋅s−2\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}; Pascal (Pa\text{Pa}) matches kg⋅m−1⋅s−2\text{kg}\cdot\text{m}^{-1}\cdot\text{s}^{-2}; Watt (W\text{W}) matches kg⋅m2⋅s−3\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}; Newton (N\text{N}) matches kg⋅m⋅s−2\text{kg}\cdot\text{m}\cdot\text{s}^{-2}.
Each derived unit is systematically expressed in terms of the fundamental SI units of mass (kg), length (m), and time (s) by substituting definitions: Newton is kg⋅m⋅s−2\text{kg}\cdot\text{m}\cdot\text{s}^{-2}, Joule is kg⋅m2⋅s−2\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}, Pascal is kg⋅m−1⋅s−2\text{kg}\cdot\text{m}^{-1}\cdot\text{s}^{-2}, and Watt is kg⋅m2⋅s−3\text{kg}\cdot\text{m}^2\cdot\text{s}^{-3}.

Step-by-Step Solution

1
Express Newton (N) in fundamental units
Force=mass×acceleration⇒1 N=1 kg⋅m⋅s−2\text{Force} = \text{mass} \times \text{acceleration} \Rightarrow 1\text{ N} = 1\text{ kg}\cdot\text{m}\cdot\text{s}^{-2}
Force is defined as mass multiplied by acceleration.
2
Express Joule (J) in fundamental units
Work=Force×distance⇒1 J=(kg⋅m⋅s−2)×m=1 kg⋅m2⋅s−2\text{Work} = \text{Force} \times \text{distance} \Rightarrow 1\text{ J} = (\text{kg}\cdot\text{m}\cdot\text{s}^{-2}) \times \text{m} = 1\text{ kg}\cdot\text{m}^2\cdot\text{s}^{-2}
Work done is force multiplied by displacement in the direction of the force.
3
Express Pascal (Pa) in fundamental units
Pressure=ForceArea⇒1 Pa=kg⋅m⋅s−2m2=1 kg⋅m−1⋅s−2\text{Pressure} = \frac{\text{Force}}{\text{Area}} \Rightarrow 1\text{ Pa} = \frac{\text{kg}\cdot\text{m}\cdot\text{s}^{-2}}{\text{m}^2} = 1\text{ kg}\cdot\text{m}^{-1}\cdot\text{s}^{-2}
Pressure is defined as force applied perpendicular to a surface per unit area.
4
Express Watt (W) in fundamental units
Power=Worktime⇒1 W=kg⋅m2⋅s−2s=1 kg⋅m2⋅s−3\text{Power} = \frac{\text{Work}}{\text{time}} \Rightarrow 1\text{ W} = \frac{\text{kg}\cdot\text{m}^2\cdot\text{s}^{-2}}{\text{s}} = 1\text{ kg}\cdot\text{m}^2\cdot\text{s}^{-3}
Power is the rate at which work is done or energy is transferred.

Key Concept

Expressing derived SI units in terms of base SI fundamental units
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Topics

Fundamental and Derived Units

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