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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 1⁄683 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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