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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

 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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