Explain with examples the derived units?
Difficulty: Hard
Derived units:
The units used to measure derived quantities are called derived units.
Derived units are defined in terms of base units and are obtained by multiplying or dividing one, or more base units from each other.
Examples:
- The unit of area (meter)^{2 }and the unit of volume (meter)^{3} are based on the unit of length, which is meter. Thus, the unit of length is the base unit while the unit of area and volume are derived units.
- Speed is defined as the distance covered in unit time; therefore, its unit is a meter per second. In the same way, the unit of density, force, pressure, power, etc. can be derived using one or more base units.
Derived quantities and their SI units with symbols
Quantity |
Unit |
||
Name |
Symbol |
Name |
Symbol |
Speed |
V |
meter per second |
ms^{-1} |
Acceleration |
A |
meter per second per second |
ms^{-2} |
Volume |
V |
cubic meter |
m3 |
Force |
F |
newton |
N or (kg m s^{2}) |
Pressure |
P |
pascal |
Pa or (N m^{-2}) |
Density |
Ρ |
kilogram per cubic meter |
Kgm^{-3} |
Charge |
Q |
coulomb |
C or (As) |
Quick Quiz
1. How can you differentiate between the base and derived quantities?
Ans: Difference between the base and derived quantities:
Base Quantities |
Derived Quantities |
i. Base quantities are the quantities based on which other quantities are expressed. |
i. The quantities that are expressed in terms of base quantities are called derived quantities |
ii. Length, mass, time, electric current, temperature, the intensity of light | and the amount of a substance. |
ii. Area, volume, speed, force, work, energy, power, electric charge, electric potential, etc. |
2. Identify the base quantity is the following:
1. Speed 2. Area 3. Force 4. Distance
The distance can be considered as a base quantity because the distance is equal to the length and its unit is a meter.
- Speed, area, and force are derived quantities because these quantities are expressed in terms of base quantities.
- Identify the following as base or derived quantity: density, force, mass, speed, time, length, temperature, and volume.
Base Quantities
Derived Quantities
Length, mass, time, temperature.
Density, volume, speed, force,
Ans
Mini Exercise
Volume is a derived quantity
1L = 1000mL
1L = 1 dm^{3}
= (10cm) ^{3}
= 1000 cm^{3}
1mL = 1 cm^{3}
Express 1 m^{3 }in liters ......... L
Solution: -1m^{3} in liters=1000L
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