Which of the following is the group of derived units?A.m,s,Pa 𝑎𝑛𝑑 Nm,s,PaandNB.Pa,N,m/s 𝑎𝑛𝑑 WPa,N,m/sandWC.k,m,kgk,m,kg and ssD.kg,K,Pa 𝑎𝑛𝑑 Nkg,K,PaandN
Question
Which of the following is the group of derived units?A.m,s,Pa 𝑎𝑛𝑑 Nm,s,PaandNB.Pa,N,m/s 𝑎𝑛𝑑 WPa,N,m/sandWC.k,m,kgk,m,kg and ssD.kg,K,Pa 𝑎𝑛𝑑 Nkg,K,PaandN
Solution
The derived units are combinations of the seven base units from the International System of Units (SI). These base units are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
Let's analyze each option:
A. m (meter), s (second), Pa (Pascal), Nm (Newton meter), and N (Newton).
- Meter and second are base units, not derived.
- Pascal is a derived unit (kg/(m·s²)).
- Newton meter is a derived unit (kg·m²/s²).
- Newton is a derived unit (kg·m/s²).
B. Pa (Pascal), N (Newton), m/s (meter per second), W (Watt).
- All of these are derived units. Pascal is kg/(m·s²), Newton is kg·m/s², meter per second is m/s (a derived unit of speed), and Watt is kg·m²/s³.
C. k (kelvin), m (meter), kg (kilogram), s (second).
- Kelvin, meter, kilogram, and second are all base units, not derived.
D. kg (kilogram), K (kelvin), Pa (Pascal), N (Newton).
- Kilogram and kelvin are base units, not derived.
- Pascal and Newton are derived units.
So, the group of derived units is option B: Pa (Pascal), N (Newton), m/s (meter per second), and W (Watt).
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