Measurement 9

Unit
1 Measurement








Have you ever purchased daily used items like rice, pulse, milk, oil, clothes,
etc. from the market? Can the shopkeepers give you all these items as
much as you want without measuring them? The shopkeepers do not give
anything without measuring. They give you things like rice, pulse, etc. by
measuring them in the kilogram (kg) unit. In the same way, they measure
oil in litre, clothes in metre and deliver you the required quantity.

In every school, the bell rings after the fixed period of time ( 45 minutes)
according to the daily class routine. Likewise, the earthquake is measured
in Richter scale.

The different physical quantities like mass, volume, length, time, magni-
tude of earthquake, etc. are measured by comparing with some standard
known quantities called units. Kilogram (kg), liter (l) metre (m), second
(s), Richter scale, etc. are some of the units of physical quantities.

The standard known quantity which is used to measure a physical
quantity is called a unit.
Types of units

The units of the physical quantities have been categorized into two groups.
They are:
1. Fundamental Units

2. Derived Units
1. Fundamental Units

The unit of mass is kilogram, the unit of time is second and the unit of
length is metre. The above mentioned physical quantities like time, mass,
length, etc. have their own existence. Similarly, their units also do not
depend upon other units as well as other units of the measurement do not
affect them. Such types of units are called fundamental units. In brief, the
fundamental units are defined as:
Those units of measurement which have their own independent existence
and do not depend upon other units are called fundamental units.




Science, Grade - 9 1

Let’s study the fundamental units from the given table:

S.N. Physical quantities Name of the Units Symbols
1. Length metre m
2. Mass kilogram kg
3. Time second s
4. Temperature kelvin K
5. Luminous intensity candela cd
6. Electric current ampere A
7. Amount of substance mole mol


















Figure no. 1. 1: Beam balance and standard masses


Different types of physical devices are used to measure the various
fundamental quantities. For example a beam balance is used to measure
mass, a watch is used to measure time, a meter scale is used to measure
length, a thermometer to measure temperature, an ammeter is used to
measure electric current and so on.

Derived Units
3
The unit of density is kg/m . It includes two fundamental units i.e.
kilogram (kg) and metre (m). In the same way, the unit of force is newton
(N) or kgms . In this unit there are three fundamental units i.e. kilogram
-2
(kg), metre (m) and second (s). The above units of density and force are
derived by the combination of two or more fundamental units. These units
fully depend on the fundamental units. Such types of dependent units are
called derived units. We can define derived units in the following way.

Those dependent units which are formed by the combination of two or
more fundamental units are called derived units.



2 Science, Grade - 9

Various derived units are used in the study of science. Let’s study some
of the important physical quantities and their derived units from the
following table:
Some physical quantities, their derived units and symbols:

Quantities Formulae Derived Units Fundamental
Units Involved

Area length × breadth metre × metre m 2

Volume length × breadth metre × metre × m 3
× height metre
Density mass kilogram Kg/m = kgm -3
3
volume metre 3

Velocity displacemen metre m/s = kgm -1
time second
Acceleration change in velocity metre m/s = ms -2
2
time second × second

Force mass × kilogram × metre kg m/s or N
2
acceleration second 2 kg ms or N
-2
or newton
Pressure force newton/metre or Kg/ms or Pa
2
2
-1 -2
area Pascal =kg m s or Pa
Work force × distance newton × metre or kgm /s or J
2
2
2 -2
Joule =kgm s or J
Power work newton × metre/ kgm /s or W
3
2
time second or watt =kg m s or W
2 -3
Moment force × distance newton × metre kgm /s =
2
2
kgm s
2 -2
Frequency 1 1 s or Hz
-1
second second or Hertz
In this way, the units which depend upon the fundamental units as well
as can be expressed in terms of fundamental units are called derived units.








Science, Grade - 9 3

Activity 1

List out the different units used Do you know?
to measure various physical A gold smith uses tola unit to measure the
quantities in your daily life. quantity of gold. Similarly, till today, in
Classify these units into two the villages, there is a traditional way of
groups, as fundamental units measuring paddy, rice, milk, ghee, etc. by
and derived units and fill in using mana and pathi.
the following table.

Fundamental Units Derived Units






Differences between fundamental and derived units

S.N. Fundamental Unit S.N. Derived Unit
They do not depend upon 1. They depend upon fundamental
other units. units.

Till today, only seven 2. Many derived units can be formed
fundamental units are used. from these seven fundamental
Examples: kilogram(kg), units.
metre (m),second(s), etc. Examples: newton(N), joule (J),
Pascal (P), watt (W), etc.
We use a unit along with a numerical value while expressing amount of
the physical quantity.

Measurement of a physical quantity = digit × unit
For example, 10 N force, 3 kg mass, etc.

SI System

To bring the uniformity in the measurement all over the world, a conference
of scientists was held in 1960 AD in Paris, the capital of France. The
conference introduced the different standard units in the measurement.
Now, these standard units are being used all over the world.

The system of measurement introduced by the Paris Conference to
bring uniformity in measurement all over the world is called SI system.
Similarly, those standard units of measurement which are introduced by
the Paris conference of the scientists held in 1960 AD are called SI units.
Its full form is System International de’units.


4 Science, Grade - 9

The Paris conference made SI
units. These SI units are used Do you know?
by all countries of the world In SI system, the mass of the cylinder,
making the measurement system made from the platinum-iridium alloy and
0
consistent worldwide. According kept at 0 C in the office of International
to the SI system, different physical Bureau of weights and measures in France
quantities are well defined is called one kilogram. The mass of this
and their models are made. cylinder is equivalent to the mass of one
liter water kept at 4 C.
0
These models are distributed to
different countries of the world
to make their prototype. On the
basis of these models and their prototypes, different physical quantities
are being measured all over the world. So, this system has played a vital
role to bring uniformity in the measurement of all the countries of the
world. All the fundamental and derived units, given in the third page are
SI units.
Why is SI unit needed? Think for a while.

You know, in Nepal, gold is measured in tola but in other countries of
the world, gold is measured in gram or kilogram. If we send three tola of
gold to America, the Americans don’t know the mass of the gold without
measuring it again and they don’t know at what cost it should be sold.
After measuring, its quantity can be known in gram and then its trade can
be done easily. It is difficult to run trade and business at international
level by using different units in different countries. So, SI unit is needed
to make the transaction easy.

Points to Remember
1. The standard known quantity which is used to measure a physical
quantity is called a unit.

2. We use a unit along with a numerical value while expressing amount
of the physical quantity, i.e. physical quantity = digit × unit

Example: mass (m) = 2 kilogram (kg)

3. Those units of measurement which have their own independent
existence and do not depend upon other units are called fundamental
units. For example; unit of length is metre (m), unit of mass is kilogram
(kg), unit of temperature is kelvin ( k), etc.
4. Those dependent units which are formed by the combination of two or
more fundamental units are called derived units. For examples; unit of



Science, Grade - 9 5

force is newton (N), unit of work is joule (J), unit of pressure is Pascal
(Pa), etc.
5. Those standard units of measurement which are introduced by the
Paris conference of the scientists held in 1960 AD are called SI units.
They are introduced to bring uniformity in the measurement all over
the world.



Exercise

(A) Tick () the correct answer from the given alternatives.

1. Which one of the following physical quantities is formed after dividing
mass by volume?

(i) Weight ( ii) Velocity (iii) Density (iv) Work

2. Which one of the following physical quantities has its S.I. unit m/s?

(i) Acceleration (ii) Velocity (iii) Force (iv) Density

3. Which one of the following is not a fundamental unit?

i) Candela (Cd) (ii) Kelvin (K) Ampere (A) (iv) Pascal (Pa)
4. Which one of the following is a derived unit?

(i) Kilogram (kg) (ii) Watt (W)

(iii) Second (s) (iv) Kelvin (K)

5. Newton is the derived unit of force. Which of the following
fundamental units are involved in it?

(i) kgm/s (ii) kgm /s (iii) kg/m s (iv) Kgm/s
2
2
2 2
2
(B) Answer the following questions.
1. What is unit? Write down the units of mass, temperature, power and
density.

2. Write any three differences between fundamental units and derived
units.

3. What is SI system? Why has SI system been developed? Give reasons.

4. What is the unit of pressure? Why is it called a derived unit? Give

6 Science, Grade - 9

reasons.

5. Why is the unit of temperature called a fundamental unit? Give reasons.

6. Find the fundamental units involved in the following derived units.

(i) Newton(N) (ii) Watt (W) (iii) Joule (J)
(iv) Pascal (Pa) (v) Cubic metre

7. The standard weights (dhaks) and meter scales of the shops in the
market are verified in every two years by the department of measurement
of Nepal, Why?




Project Work

Search the different types of units used in your village or city from past to
till today. Fill the findings in the table shown below. Which unit would be
more reliable between the old one and the new one? Give reasons.

Physical Units Used in the Past Units Being Used at Present
Quantities
Length
Mass

Time

Glossary

Unit = the standard known quantity

Frequency = the number of waves produced in one second






















Science, Grade - 9 7