Physics

Unit and Dimension

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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 = 10³kg

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

Dimensions 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 the 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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