** **

**
UNITS AND DIMENSIONS**

By international agreement a small number of physical quantities such as length,
time etc. are chosen and assigned standards. These quantities are called ‘base
quantities’ and their units as ‘base units’. All other physical quantities are
expressed in terms of these ‘base quantities’. The units of these dependent
quantities are called ‘derived units’.

The standard for a unit should have the following characteristics.

(a) It should be well defined.

(b) It should be invariable (should not change with time)

(c) It should be convenient to use

(d) It should be easily accessible

The 14th general conference on weights and measures (in France) picked seven
quantities as base quantities, thereby forming the International System of Units abbreviated as SI (System de International) system.

__Base quantities and their units__

The seven base quantities and their units are

Base quantity
Unit Symbol

Length Metre M

Mass
Kilogram Kg

Time Second
Sec

Electric current Ampere A

Temperature Kelvin
K

Luminous intensity Candela Cd

Amount of substance Mole
Mole

__DERIVED UNITS__

derived units are those units which can be expressed in
terms of base units. For example, speed is defined to be the ratio of

distance to time.

Unit of Speed = (unit of distance (length))/(unit of
time) = m/s = ms-1 (Read
as metre per sec.)

__ SOME DERIVED SI UNITS AND THEIR SYMBOLS
__

Quantity Unit
Symbol Expressed in base units__
__Force newton N
Kg-m/sec2

Work
joules J
Kg-m2 /sec2

Power watt
W
Kg-m2 /sec3

Pressure pascal Pa
Kg m-1/S2

**IMPORTANT**

__
__The following conventions are adopted while writing a unit.

(1) Even if a unit is named after a person the unit is not written IN capital letters. i.e. we write joules not Joules.

(2) For a unit named after a person the symbol is a capital letter e.g. for joules we write ‘J’ and the rest of them

are in lowercase letters e.g. seconds is written as ‘s’.

(3) The symbols of units do not have plural form i.e. 70 m not 70 ms or 10 N not 10Ns.

(5) Punctuation marks are not written after the unit

e.g. 1 litre = 1000 cc not 1000 c.c.

It has to be borne in mind that SI system of units is not
the only system of units that is followed all over the

world. There are some countries (though they are very few in number) which use
different system of units. For

example: the FPS (Foot Pound Second) system or the CGS (Centimeter Gram Second)
system.

__DIMENSIONS__

The unit of any derived quantity depends upon one or more
fundamental units. This dependence can be expressed with

the help of dimensions of that derived quantity. In other words, the dimensions
of a physical quantity shows how its

unit is related to the fundamental units.

To express dimensions, each fundamental unit is represented by a capital letter.
Thus the unit of length is denoted

by L, unit of mass by M. Unit of time by T, unit of electric current by I, unit
of temperature by K and unit of

luminous intensity by C.

Remember that speed will always remain distance covered per unit of time,
whatever is the system of units, so the

complex quantity speed can be expressed in terms of length L and time T. Now, we
say that dimensional formula of

speed is LT-1. We can relate the physical quantities to each other (usually we
express complex quantities in terms

of base quantities) by a system of dimensions.

Dimension of a physical quantity are the powers to which the fundamental
quantities must be raised to represent the

given physical quantity.

Example:

Density of a substance is defined to be the mass contained in unit volume of the
substance.

Hence, [density] = ([mass])/([volume]) = M/L3 = ML-3

So, the dimensions of density are 1 in mass, -3 in length and 0 in time.

Hence the dimensional formula of density is written as

[ρ]= ML-3T0

It is to be noted that constants such as ½ π, or trigonometric functions such as
“sin wt” have no units or

dimensions because they are numbers, ratios which are also numbers.

Units and Dimensions are important from IIT JEE perspective. Objective questions
are framed on this section. AIEEE

definitely has 1-2 questions every year directly on these topics. Sometimes both
IIT JEE and AIEEE do not ask

questions on units and dimensions directly but they change units and involve
indirect application. So it’s very

important to master these concepts at early stage as this forms the basis of
your preparation for IIT JEE and AIEEE

Physics.