Dimensional Analysis of Quantity

Dimensional Analysis Of Quantity

The seven basic quantities lead to a number of derived quantities such as pressure, volume, force, density, speed etc. The units for such quantities can be obtained by defining the derived quantity in terms of the base quantities using the base units. For example, speed (velocity) is expressed in distance/time. So the unit is m/s or ms-1. The unit of force (mass×acceleration) is kgms-2 and the unit for acceleration is ms-2.

 Table: Derived Units

Physical quantity

Unit

Symbol

Area

square metre

m2

Volume

cubic metre

m3

Velocity

metre per second

ms–1

Acceleration

metre per second square

ms–2

Density

kilogram per cubic metre

kg m–3

Molar mass

kilogram per mole

kg mol–1

Molar volume

cubic metre per mole

m3 mol–1

Molar concentration

mole  per cubic metre

mol m–3

Force

newton (N)

kg m s–2

Pressure

pascal (Pa)

N m–2

Energy work

joule (J)

kg m2 s–2, Nm

Table: Standard prefixes use to reduce the basic units

Multiple Prefix Symbol Submultiple Prefix Symbol
1024 yotta Y 10–1 deci d
1021 zetta Z 10–2 centi c
1018 exa E 10–3 milli m
1015 peta P 10–6 micro m
1012 tera T 10–9 nano n
109 giga G 10–12 pico p
106 mega M 10–15 femto f
103 kilo k 10–18 atto a
102 hecto h 10–21 zeto z
101 deca da 10–24 yocto y

 

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