What do you mean by Dimensional Analysis (Derived units)?
From the seven basic or fundamental units, the units of some other physical quantities such as area, volume, pressure, force, speed, velocity etc. can be derived. These are called derived units. Derived unit of a physical quantity is also called dimensional formula of that quantity. For example, the unit of area can be derived as: Area = Length × Breadth If length = 6 m and breadth = 5m, then Area = 6m × 5m = 30m2
Unit for area is m2
Some common derived units are listed below:
Derived Units
|
Physical Quantity |
Units |
Symbol for Unit |
Definition in S.I. Basic Units |
|
Area |
square metre |
m2 |
m2 |
|
Volume |
cubic metre |
m3 |
m3 |
|
Density |
kilogram per cubic |
kg/m3 or kg m–3 |
|
|
Speed |
metre per second |
m/s or ms–1 |
|
|
Acceleration |
metre per second |
||
|
Force |
newton |
N |
kg ms–2 |
|
Pressure |
pascal |
Pa |
kg m–1s–1 or Nm–2 |
|
Energy |
joule |
J |
kg m2 s–2 |
|
Frequency |
hertz |
Hz |
s–1 |
|
Electric charge |
coulomb |
C |
A Sec = amp second |
|
Electric resistance |
ohm |
Ω |
m2 kg s–3 A–2 |
|
Electric potentialdifference |
volt |
V |
kg m2 s–3 A–1 or JA–1 S–1 |
