Units for measurement

Category : JEE Main & Advanced

* Units for measurement             

The chosen standard of measurement of a quantity which has essentially the same nature as that of the quantity is called the unit of the quantity. Following are the important types of system for unit,           

(1) C.G.S. System : Length (centimetre), Mass (gram), Time (second)           

(2) M.K.S. System : Length (metre), Mass (kilogram), Time (second)           

(3) F.P.S. System  : Length (foot), Mass (pound),      Time (second)           

(4) S.I. System : The 11th general conference of weights and measures (October 1960) adopted International system of units, popularly known as the SI units. The SI has seven basic units from which all other units are derived called derived units. The standard prefixes which helps to reduce the basic units are now widely used. Dimensional analysis : 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 \[m{{s}^{-1}}\]. The unit of force \[\text{(mass}\times \text{ acceleration)}\] is \[kg\ m{{s}^{-2}}\] and the unit for acceleration is \[m{{s}^{-2}}\].

Seven basic S.I. units

Length Mass Time Temperature Electric Current Luminous Intensity Amount of substance
metre (m) Kilogram (kg) Second (s) Kelvin (K) Ampere (A) Candela (Cd) Mole (mol).

 

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.

 

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.

       

Conversion factors

1 m = 39.37 inch 1 cal = 4.184 J 1 e.s.u. = 3.3356 ´ 10?10 C 1 mole of a gas = 22.4 L at STP
1 inch = 2.54 cm 1 eV = 1.602 ´ 10?19 J 1 dyne = 10?5 N 1 mole a substance = N0 molecules
1 litre = 1000 mL 1 eV/atom =96.5 kJ mol?1 1 atm = 101325 Pa 1 g atom = N0 atoms
1 gallon (US) = 3.79 L 1 amu = 931.5016 MeV 1 bar = 1 ´ 105 N m?2 t (oF) = 9/5 t (oC) + 32
1 lb = 453.59237 g 1  kilo watt hour = 3600 kJ 1 litre atm = 101.3 J 1 g cm?3 = 1000 kg m?3
1 newton =1 kg m s?2 1 horse power = 746 watt 1 year = 3.1536 ´ 107 s 1Å = 10?10 m
1 J = 1 Nm =1 kg m2 s?2 1 joule = 107 erg 1 debye (D) = 1 ´ 10 ?18 esu cm 1nm = 10?9 m.



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