Unit and Dimension

Unit:

The chosen standard used for measuring a physical quantity is called unit.

The unit should be:

1. Well defined

2. Easy to reproduce

3. Easy to compare

4. Internationally accepted independent of changes in physical conditions

Units are of two types:

1. Fundamental Unit and

2. Derived Unit

System of Units:

Units depend on choice. Each choice of units leads to a new system (set) of units. The internationally accepted systems are: 1. CGS system 2. MKS System 3. FPS System 4. SI Units.

In SI Units, there are seven fundamental units given in the following table:

Physical Quantity

SI Unit

Symbol

Length

metre

m

Mass

kilogram

kg

Time

second

s

Electric Current

ampere

A

Temperature

kelvin

K

Luminous intensity

candela

1 cd

Amount of substance

mole

mo!

Besides these seven fundamental units, two supplementary units are also defined, viz., radian [rad] for plane angle and steradian (sr) for solid angle.

  • All the units which are defined / expressed in terms of fundamental units are called derived units.

Some important derived units

S.

Physical Quantity

Cgs units

SI unit

Relation

1.

Force

Dyne

Newton

1 newton = 105 dyne

2.

Work

Erg

Joule

1 joule = 107 erg

Some practical units of length mass and time

 

 

Length

Light year = distance traveled by light in one year vacuum.

1LY = 9.46 x 1015m

1 Astronomical Unit (A.U.) = 1.5 x 1011 m

1 Parsec = 3.26 ly = 3.08 x 1016 m

1 Nautical mile or Seamile = 6076 ft = 1852 m

1 Micron = 1 μm = 10-6 m

1 Angstron (A) = 10~10 m

 

 

 

Mass

1 Quintal = 102 kg

1 Metric ton = 10kg

1 Atomic Mass Unit (amu) or Dalton = 1.66 x 10-27 kg

1 Slug = 14.59 kg

1 Pound = 0.4537 kg 

1 Chandrashekhar limit = 1.4 times the mass of sun = 2.8 x 1030 kg

 

 

Time

1 Solar day = 86400 sec.

1 Year = 365 1/2 solar days

1 Lunar month = 27.3 solar days.

Tropical year = It is the year in which total solar eclipse occurs.

Leap year = It is the year in which the month of February is of 29 days.

  • Astronomical distances are measured in light year because speed of light is always the same.

Prefixes used in metric system

Prefix

Symbol

Multiplier

deci

d

{10^-^1}

centi

c

{10^-^2}

milli

m

{10^-^3}

micro

μ 

{10^-^6}

nano

n

{10^-^9}

pico

P

10{^-{^1^2}

femto

f

10{^-{^1^5}

atto

a

10{^-{^1^8}

zepto

z

10{^-{^2^1}

yocto

y

10{^-{^2^4}

deca

da

10{^-{^1}

hecto

h

10{^-{^2}

kilo

k

10{^-{^3}

mega

M

10{^-{^6}

giga

G

10{^-{^9}

tera

T

10{^-{^1^2}

peta

P

10{^-{^1^5}

exa

E

10{^-{^1^8}

zetta

Z

10{^-{^2^1}

yotta

Y

10{^-{^2^4}

Dimension

Dimension of a physical quantity are the powers through which different fundamental quantities are raised to define the quantity.

The expression by which a physical quantity is defined in terms of fundamental quantities is called dimensional, formula of the quantity.

For example: Dimensional formula of momentum is MLT-1

S.

Quantity

Dimensional Formula

1

Volume

[M^0L^3T^0]

2

Density

ML^{-3}T^0

3

Velocity

\dpi{100} \fn_jvn [M^0L^1T^{-1}]

4

Acceleration

[M^0L^1T^{-2}]

5

Angular Velocity, Frequency

[M^0L^0T^{-1}]

6

Momentum, Impulse

[MLT^{-1}]

7

Force

[MLT^{-2}]

8

Work, Energy

[ML^2T^{-2}]

9

Power

[ML^2T^{-3}]

10

Pressure, Streess, Modulus of Elasticity

[ML^{-1}T^{-2}]

11

Moment of Inertia

[ML^2T^0]

12

Torque/Moment of Force

[ML^2T^{-2}]

13

Angular Momentum, Planck’s Constent

[ML^2T^{-1}]

14

Coefficient of Viscosity

[ML^{-1}T^{-1}]

15

Surface Tension

[M^1L^0T^{-2}]

16

Universal Gravitational Constant

[M^{-1}L^3T^{-2}]

17

Latent Heat

[M^0L^2T^{-2}]

18

Specific Heat

[M^0L^2T^{-2}K^{-1}]

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