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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

MultiplePrefixSymbolSubmultiplePrefixSymbol
1024yottaY10–1decid
1021zettaZ10–2centic
1018exaE10–3millim
1015petaP10–6microm
1012teraT10–9nanon
109gigaG10–12picop
106megaM10–15femtof
103kilok10–18attoa
102hectoh10–21zetoz
101decada10–24yoctoy

 

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