Units of Measurement

Unit of measurement- These are also some systems for units:

(1) C.G.S. System: Length (centimeter), 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)]

The international system of units (S.I.Units) - All physical quantities have to be measured. The value of a physical quantity is expressed as the product of the numerical value and the unit in which it is expressed.

The unit is defined as the standard or reference chosen to measure any physical quantity.

Fundamental Units: fundamental units are not those units which can be derived from one another nor they can be further resolved into any other units.

The seven basic physical quantities on which the international system of units is based, their symbols, the names of their units (called the basic units) & the symbols of these units are given in table 1-

 Physical Quantity SI unit Symbol Mass Kilogram Kg Length Meter m Temperature Kelvin K Amount of substance Mole Mol Time Second S Electric current Ampere A Luminous intensity Candela Cd

Extra Notes-

The Kilogram has been defined as the mass of Platinum-Iridium cylinder that is stored air tight jar at international bureau of weights & measure in France.

The metre is defined by CGPM as the length of the path travelled by light in the vaccume during a time interval of 1/299,792,458 of a second.

The second is duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of caesium-133 atom.

The Kelvin is taken as equal to the fraction 1/273.16 of the triple point of water.

The ampere is that constant current which ,if maintained in the two straight parallel infinite length of negligible circular cross section & placed 1 meter apart in vaccume, would produce between these conductors a force equal to 2 x 10-7  Newton per meter of length.

The mole is the amount of a substance that contains as in 12 gram of pure carbon-12.

The candela is the luminous intensity, The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1683 watt per steradian.

Derived unit: The units of all other physical quantities which are derived from the units of these basic physical quantities are known as derived units.

Some commonly used quantities & their derived units are given in table 2

 Physical Quantity Unit symbol Defination Velocity (v) Metre per sec ms-1 Distance/unit time Area (A) Square metre m2­ Length square Volume (V) Cubic metre m3 Length Cube Density (r) Kilogram m-3 Kg m-3 Mass/unit volume Energy (E) Joule (J) Kg m2s-2 Force. distance Force (F) Newton (N) Kg ms-2 Mass. Acceleration Frequency (n) Hertz Cycle per sec Cycles/sec Pressure (P) Pascal (Pa) Nm-2 Force/unit area Electrical charge Coulomb (C) A-s (ampere - second) Current. Time Potential difference Volt Kgm2s-3A-1=JA-1s-1=JC-1 - Electric resistance ohm VA-1 Pott.diff/current Electric conductance ohm-1 AV-1 Reciprocal of resistance

Subsidiary Units-Some time we requires units that may be multiply or fractions of base units are known as subsidiary units. The SI system recommends the multiples like 102,104,106 or fraction like 10-2, 10-4, 10-6 i.e. these powers is multiples of 2.These are indicated by special prefixes. Some multiples & their prefixes are given in table 3:

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

Points to be remember-1.The unit is written always in small letter of starting word, e.g.unit of work is written as joule, not as Joule.

2. Symbols of unit don't have plural ending like 10 cm is correct not 10cms.

3. Words & symbols should not be mixed e.g. we should write m s-1 or meter sec-1 not meter s-1.

4. Prefixes are used with base unit.

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