S01-L03-SI Units

Goals of this Lecture
© Prof. Mukesh N Tekwani
S01-L03 SI and CGS Units
Learn about SI
and CGS units
Convert from SI to
CGS and vice-
versa
Apply these units
to various physical
quantities

Measurement of Physical Quantity
Every physical quantity is made up of two parts:
1. A number
2. A unit
Why is a unit important? Let’s say you see a pretty dress in a shop and the price
mentioned is 200. See, the currency symbol is not mentioned. So is the price
$100, or £ 200 or Rs. 200? You know that the currency changes the cost. So here,
the currency becomes the ‘unit’.
Physics deals with measurable quantities. Most physical quantities have units
The standard unit of measuring length is metre. The standard unit of measuring
time is second . The standard unit of measuring mass is kilogram

What is a unit?
A unit is a standardized value.
Whenever we want to measure something, there must be a fixed standard against
which we can compare it.
For example, if you want to buy one kilogram of a vegetable, the one kilogram
must weigh the same in every shop.
Similarly if you have to wait for someone for 5 minutes, the time of 5 minutes is
the same for everyone.
And the same way, if a person’s height is 162 cm, it means all people with that
height will be equally tall.

How are units standardized?
There is an International System of Units which is an internationally agreed upon
system. So all countries have agreed to the system of units.
This system of units is called the SI System. SI stands for the French term Système
International d'unites, and this system has been used worldwide since 1960.
All countries have agreed upon these things: how heavy should a kilogram be,
how long (or high) should a metre be, and how much time should 1 minute
represent. So no matter where you go in the world, a kilogram, a metre, and a
second will mean the same thing. This is called standardisation.

Types of physical quantities
These quantities donot depend upon other
physical quantities for their measurement.
These are also called base quantities
Fundamental Physical
Quantities
These quantities depend on other physical
quantities for their measurement.
Derived Physical
Quantities

S01-L03 SI Units
Fundamental Physical Quantities and their SI Units
Fundamental
Quantity
Symbol SI Unit Unit symbol
Length l metre m
Mass m kilogram kg
Time t second s
Electric Current I ampere A
Temperature T kelvin K
Amount of substance n mole mol
Luminous Intensity IV candela cd

S01-L03 CGS Units
Fundamental Physical Quantities and their CGS Units
Fundamental
Quantity
Symbol CGS Unit Unit symbol
Length l centimetre cm
Mass g gram g
Time t second s
CGS stands for Centimetre-Gram-Second.
Generally, in the laboratory experiments, we use the CGS system since physical
quantities being measured are small.

Conventions adopted while writing a unit
➢ Even if a unit is named after a person, the unit is not written in capital letters.
E.g., we write joule, not Joules
➢ If a unit is named after a person, the symbol is a capital letter. E.g., J for joule,
N for Newton.
➢ The symbols of units do not have a plural form. E.g., 80 m (for 80 metres), or
30 ms (for 30 milli seconds), 10 N (for 10 newton)
➢ Punctuation marks are not written after the unit. E.g., 1 litre = 1000 cc and not
as 1000 c.c.

S01-L03 SI Units
Derived Quantity Symbol Formula Unit
symbol
Area A A = length x length m2
Volume V V = length x length x
length
m3
Density d d = mass / volume kg/m3
Derived units such as m2 and kg/m3 consist of combination of base units.
The base units may be multiplied together or divided by one another but they
are NEVER added or subtracted.
Some Derived Physical Quantities and their SI units

S01-L03 Fundamental and Derived Quantities – Quick Quiz 1
1. Is the following statement true or false?
“Fundamental physical quantities such as mass, length and time
depend on other physical quantities for their measurement”.
2. Is the following statement true or false?
“Derived physical quantities such as area, density, volume and others
depend on other physical quantities for their measurement”.

S01-L03 Relation between SI and CGS units
Fundamental
Quantity
SI Unit CGS Unit Relation
SI to CGS
Relation
CGS to SI
Length m cm 1 m = 100 cm 1 cm = 0.01 m
Mass kg g 1 kg = 1000 g 1 g = 0.001 kg
Time s s s ----
SI and CGS system measure the same physical quantities but the units are
different. This relation is shown below for three fundamental physical quantities.
The unit of time is the same in both SI and CGS systems

Can you name some fundamental physical quantities?
✓ Length
✓ Mass
✓ Time
Can you name some derived physical quantities?
✓ Area
✓ Volume
✓ Density
✓ Pressure
✓ Work
✓ Current……
S01-L03 SI and CGS units – Quick Quiz 2
Remember: Physical quantities such as length,
width, breadth, height, distance, radius,
diameter, perimeter and displacement are
equivalent to length.

Complete the table below by writing the SI units or names of physical quantities
that they measure.
Quantity Length Time Current Temperature
SI Unit kg cd mole

Complete the table by converting from SI to CGS or CGS to SI units
SI Unit 1 m 10 m 10 kg 60 s 0.1 kg
CGS Unit 30 s 10 g

What are the base units of speed?
What do we mean by ‘base units’? Base units means fundamental units. So when
you are asked to state the base units, it means find the unit of the physical
quantity such that the unit involves only the 7 fundamental units.
Speed is defined as the distance travelled per unit time.
𝑠𝑝𝑒𝑒𝑑 =
ⅆ𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑖𝑚ⅇ
So the unit of speed is m/s. This involves 2 fundamental or base units. Hence m/s
is called the base unit of speed. This can also be written as m s-1

Determine the units of the following quantities:
1. Area
Area = length x width
2. Volume
Volume = length x width x height

1. Density (or, volume density)
𝑑ⅇ𝑛𝑠𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
2. Speed
spⅇⅇⅆ =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑖𝑚𝑒

1. Acceleration
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑡𝑖𝑚𝑒
2. Momentum
momentum = mass x speed

1. Force
𝑓𝑜𝑟𝑐𝑒 = 𝑚𝑎𝑠𝑠 𝑥 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
2. Pressure
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
𝑓𝑜𝑟𝑐𝑒
𝑎𝑟𝑒𝑎

1. Linear density or Mass per unit length
𝐿𝑖𝑛𝑒𝑎𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑀𝑎𝑠𝑠
𝑙𝑒𝑛𝑔𝑡ℎ
2. Work
𝑤𝑜𝑟𝑘 = 𝑓𝑜𝑟𝑐𝑒 x 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

The table below gives the volumes and masses of four objects. Which object has
the greatest density?
Object Mass /g Volume /cms3
A 5.5 2.0
B 13 3.0
C 15 7.0
D 18 5.0

a) Which of the above are units of mass? ______________________
b) Which of the above are units of length? ______________________
c) Which of the above are units of time? ______________________
d) Which of the above are units of density? ______________________
e) Which of the above are units of volume? ______________________
kg g mm cm s m3 km m μs
kg / m3 mg ml g / cm3 ns ms cm3 m2 cm2

Which of the following physical quantities is not a base (fundamental) quantity?
a) Weight
b) Temperature
c) Time
d) Electric current
S01-L03 SI an CGS Units – Quick Quiz 13

The prefixes according to their value in ascending order are:
a) micro, milli, centi, kilo
b) mega, giga, kilo, centi
c) centi, giga, micro, milli
d) giga, mega, kilo, centi
S01-L03 SI and CGS Units – Quick Quiz 14

Which is a pair of SI base units?
a) metre and newton
b) coulomb second
c) kilogram and kelvin
d) ampere joule
S01-L03 SI and CGS Units – Quick Quiz 15

Column A gives name of derived quantity, column B contains the formula (or
relationship with other quantities). Write the derived unit for each in column C.
Derived Quantity Formula Derived unit
Area Area = length x width m2
Volume Volume = length x width x height
Speed Speed = distance / time taken
Acceleration Acceleration = change in speed / time
Density Density = mass / volume
Force Force = mass x acceleration
Work Work = force x displacement
Power Power = work / time
Momentum Momentum = mass x velocity

Column A gives name of base (fundamental) quantity, column B contains the
name of the base unit, and column C contains the symbol for the unit. Complete
the table.
Base Quantity Base unit Symbol
Length Metre m
Mass
Time
Electric Current
Temperature
Luminous Intensity
Amount of substance Mole mol

S01-L05 SI Units to CGS Units conversion
Sometimes in a numerical problem, certain physical quantities are given in SI unit
and some other quantities are given in CGS Units. Before substituting the vales in
the formula, you must convert all physical quantities to the same unit.
Let us now see some examples to convert from SI unit to CGS unit. To understand
this part, you must remember at least the following conversions:
For length: 1 m = 100 cm
For mass: 1 kg = 1000 g
1. Convert 2 kg to gm. 2 kg = 2 x 1000 g = 2000 g
2. Convert 5 m to cm. 5 m = 5 x 100 cm = 500 cm

S01-L05 CGS Units to SI Units conversion
We will now study some examples to convert from CGS unit to SI unit. To
understand this part, you must remember the following conversions:
For length: 1 cm = 10-2 cm
For mass: 1 g = 10-3 g
1. Convert 50 g to kg.
50 g = 50 x 10-3 kg = 5 x 10-2 kg
2. Convert 67 cm to m.
67 cm = 67 x 10-2 m = 0.67 m = 6.7 x 10-1 m

S01-L05 CGS Units to SI Units conversion
This problem involves converting speed from km/h to m/s
Remember the following:
For time: 1 h = 60 min
1 m = 60 s
1. Convert the speed of 25 km/h to m/s
25 km/h = 25 x 1000/(1 x 60 min x 60) = 25 000/3600 = 0.69 m/s

S01-L05 SI Units – Quick Quiz 18
An aluminium cylinder has a volume of 300 cm3 and a mass of 810 g. Calculate the
density of aluminium.
Density =
𝑚𝑎𝑠𝑠
Density =
810
300
So, density = 2.7 𝑔/𝑐𝑚3

The mass of a gold ring is 84 g and density of gold is 19.3 g/cm3. Calculate the
volume of the gold ring.
Density =
𝑚𝑎𝑠𝑠
Volume =
𝑚𝑎𝑠𝑠
𝑑𝑒𝑛𝑠𝑖𝑡𝑦
=
84
19.3
= 4.4 cm3
So, volume of the gold ring = 4.4 𝑐𝑚3

Calculate the density of a piece of wood measuring 30 cm x 10 cm x 10 cm and of
mass 2.25 kg. Give your answer in (a) g cm-3 , and (b) kg m-3 .
Volume = 30 cm x 10 cm x 10 cm = 3000 cm3.
In SI units, Volume = 3000 x 10-2 m x 10-2 m x 10-2 m = 3 x 10-3 m3 .
Density =
𝑚𝑎𝑠𝑠
Density =
2.25 𝑥 1000
3000 = 0.75 g cm-3
Density =
2.25
3 x 10−3 = 0.75 x 103 kg m-3

Which of the following can 13 hours and 45 mins be written as?
(A) 13.45 hr
(B) 7.80 x 102 min
(C) 4.95 x 104 s
(D) 4.95 x 104 ms

An athlete takes 9 mins to complete a 2.5 km race. What is her average speed?
(A) 4.6 m s-1
(B) 277 m s-1
(C) 41.6 m s-1
(D) 46 m s-1

A sample of ethanol has a volume of 210 cm3. Its density is known to be 0.79
g/cm3. What is the mass of this volume of ethanol?
Density =
𝑀𝑎𝑠𝑠
𝑉𝑜𝑙𝑢𝑚𝑒
So, mass = density x volume
∴ mass = 0.79 g/cm3 x 210 cm3
∴ mass = 165.9 g

Calculate the density of mercury if 500 cm3 has a mass of 6.80 kg. Give your
answer in g/cm3.
Density =
𝑀𝑎𝑠𝑠
∴ density =
6800 𝑔
500 𝑐𝑚3
∴ density = 13.6 g/cm3

A piece of iron has a mass of 380 kg and a volume of 0.05 m3. Calculate its density.
Give your answer in g/cm3.
Density =
𝑀𝑎𝑠𝑠
∴ density =
380 𝑘𝑔
0.05 𝑐𝑚3
∴ density = 7600 kg/cm3
Note: Steel is an alloy of iron and other elements. Its density can vary between
7750 kg/m3 and 8050 kg /m3.

Prof. Mukesh N Tekwani
S01-L03 SI and CGS units

S01-L03-SI Units

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