# Physical Quantity Measuring System

## What are called Physical quantities?

A physical quantity is defined as that quantity which can be measured directly or indirectly by comparing it with standards or gauging with other measurable quantity.

A Physical quantity may be a fundamental quantity or a derived quantity. The physical quantities are the building blocks of physics in terms of which all the basic laws of physics can be expressed in mathematical forms.

EXAMPLE –

Length, mass, temperature, speed, force, electric current etc. are some examples of physical quantities.

Thus, a physical quantity must have –

1. A numerical value of measurement.
2. An unit for measurement.

EXAMPLE

Mass is a physical quantity which can be quantified as ( n \ kg ) , where ( n ) is the numerical value of measurement and ( kg ) is the unit of measurement.

## Types of Physical Quantities

Physical quantities are of two types –

1. Fundamental quantity.
2. Derived quantity.

### 1. Fundamental Physical Quantity

Fundamental physical quantities are those physical quantities which are independent of other physical quantities. Being independent these quantities are not required to define in terms of any other quantities. Hence, these quantities are also called base quantities.

A fundamental quantity must be easily measurable. We need a minimum of seven fundamental quantities. These are –

1. Mass.
2. Length.
3. Time.
4. Temperature.
5. Electric current.
6. Luminous intensity.
7. Amount of substance.

### 2. Derived Physical Quantity

Derived physical quantities are those quantities which are dependent of other quantities. These quantities are required to define in terms of (1) two or more fundamental physical quantities or (2) a mixture of two or more fundamental and derived quantities both.

All physical quantities other than above mentioned seven fundamental quantities are derived quantities.

EXAMPLE –

1. Area or volume are expressed in terms of product of two or more length which is a fundamental quantity. Hence area or volume are derived quantities.
2. Velocity is expressed in terms of length and time. Both are fundamental quantities. Hence velocity is a derived quantity obtained from multiplication of two fundamental quantities.
3. Acceleration is expressed in terms of velocity which is a derived quantity and time which is a fundamental quantity. Hence acceleration is also a derived quantity.
4. Momentum is expressed in terms of mass which is a fundamental quantity and velocity which is a derived quantity. Hence momentum is also a derived quantity.

TO BE NOTED –

Electric current is defined in terms of two different fundamental quantities which are (i) number of charges flowing through conductor and (ii) time. Though it is considered as a fundamental quantity.

Reason – This is because, current can be measured more easily than counting the number of charges flowing through a conductor. We can measure a current easily by using Ammeter but counting of charges flowing through the conductor is not so easy.

A fundamental quantity must be easily measurable. Therefore, electric current is considered as a fundamental quantity instead of charge.

## Units of measurement of Physical Quantity

A standard amount of a physical quantity chosen to measure the physical quantity of the same kind is called a physical unit.

Units are of two types –

1. Fundamental units – Units used to measure fundamental physical quantities are called fundamental units e.g. metre, millimeter, gram, kilogram, second etc. are fundamental units.
2. Derived units – Units used to measure derived physical quantities are called derived units e.g. square meter, cubic centimeter, litre, newton, joule etc. are derived units.

### Systems of Units

A complete set of units which is used to measure all kinds of fundamental and derived quantities of is called a system of units.

Some of most commonly used systems of units are as follows –

1. CGS System – It was set up in France. It is based on centimeter, gram and second as the fundamental units of length, mass and time respectively.
2. FPS system – It is a British system based on foot, pound and second as the fundamental units of length, mass and time respectively.
3. MKS system – It is also a French system based on meter, kilogram and second as the fundamental units of length, mass and time respectively.
4. SI system – It is the international system of units. It is a modernized and extended form of the metric systems like CGS and MKS systems. It covers all branches of science and technology.

### Units in different systems

Units for important fundamental quantities –

Units of measurement of fundamental quantities in CGS and SI systems are given as follows –

 Sl. No. Physical quantity Unit in CGS system Unit in SI system 1 Mass gram kilogram 2 Length centimeter metre 3 Time second second 4 Temperature degree centigrade degree kelvin 5 Electric current Biot ampere 6 Luminous Intensity — candela 7 Amount of substance gram-mole gram-mole

Units for important derived quantities –

Units for some important derived quantities in CGS and SI systems of measurements are given below –

 Sl. No. Physical quantity Unit in CGS system Unit in SI system 1 Force dyne newton 2 Pressure barye pascal 3 Momentum g cm s-1 kg m s-1 4 Work erg joule 5 Energy erg joule 6 Power erg s-1 joule s-1 or watt 7 Viscosity dyne s cm-2 or poise newton s m-2 or decapoise 8 Gravitational constant dyne cm2 g-2 newton m2 kg-2 9 Gravitational field dyne g-1 newton kg-1 10 Gravitational potential erg g-1 joule kg-1 11 Magnetic pole strength unit pole ampere metre or newton per tesla 12 Magnetic intensity or Intensity of magnetic field gauss tesla or newton per ampere per metre 13 Magnetic flux maxwell weber 14 Magnetic flux density gauss weber m-2 or tesla 15 Electric charge franklin Coulomb 16 Electric dipole moment debye coulomb metre 17 Electric field or Intensity of electric field — volts per metre or newton per coulomb ( N C-1 ) 18 Electric flux — volt metre or newton m2 coulomb-1 19 Capacitance centimeter coulomb per volt or farad 20 Inductance abhenry henry

Advantages of SI units over other system of units of measurements are –

1. SI system is a coherent system of units. – All derived units can be obtained by simple multiplication or division of fundamental units without introducing any numerical conversion factor.
2. SI system is a rational system of units. – It uses only one unit for a given physical quantity in different forms. For example, all forms of energy are measured in joule. On the other hand, in MKS system, the mechanical energy is measured in joule, heat energy in calorie and electrical energy in watt hour.
3. SI system is a metric system. – The multiples and sub multiples of SI units can be expressed as powers of 10 .
4. SI system is an absolute system of units. – It does not use gravitational units. The use of gravitational acceleration 'g' is not required.
5. SI system is an internationally accepted. – It is the internationally accepted system of units.

### Symbolic representation of SI Units

Some specific rules and guidelines are followed for writing SI units in symbolic form. These are –

1. Only small letters are used for symbols of units.
2. Symbols are not followed by a full stop.
3. The initial letter of a symbol is capital only when the unit is named after a scientist.
4. The full name of a unit always begins with a small letter even if it has been named after a scientist. Example – unit of force is written as “newton” but its symbol is “N”.
5. Symbols do not take plural form.

## Practical units of Physical Quantities

SI system of units are most popular for measurement of physical quantities and are universally accepted worldwide. But in some cases, practical units are commonly used for expressing quantities which are too small or too large in measurement. Some of these practical units are stated below.

### Practical Units for Length

(1) Fermi –

It is the practical unit for measurement of very small distances used for measuring nuclear sizes. It is also called femtometre.

1 \text {fermi} = 1 \text {fm} =  10^{-15} \ m

The radius of a proton is 1.2 \ \text {fermi}

(2) Angstrom –

It is the practical unit for measurement of small distances used to express wavelength of light.

1 \ \text {angstrom} = 1 \ Å = 10^{-10} \text {m}

(3) Nanometre –

Nanometre is the practical unit for measurement of small distances. It also used for expressing wavelength of light.

1 \ \text {nanometer} = 1 \text {nm} = 10^{-9} \text {m}

(4) Micron –

Micron is the practical unit for measurement of small distances. It is commonly used in biological science to define the size of cells and cell organelles. Mostly it is also called as micrometre.

1 \ \text {micron} = 1 \ \mu \ m = 10^{-6} \ m

(5) Light year –

Light year is the practical unit for measurement of very large distances. It is the distance traveled by light in one year in vacuum medium. This unit is used to define the distance between planets and stars in astronomy.

1 \ \text {light year} = 3 \times 10^8 \ m \ s^{-1} \times 365.25 \times 24 \times 60 \times 60 \ s

Or, \quad 1 \ \text {ly} = 9.467 \times 10^{- 15} \ m

Because speed of light in vacuum is ( 3 \times 10^{8} \ m \ s^{-1}

(6) Astronomical unit –

Astronomical unit is the practical unit for measurement of very large distances. It is defined as the mean distance of the earth from the sun. This unit is also used in astronomy to measure the distances of planets.

1 \ \text {astronomical unit} = 1 \text {AU} = 1.496 \times 10^{11} \ m

(3) Parsec (parallactic second)

It is the largest practical unit of distance used in astronomy. It is defined as the distance at which an arc of length ( 1 \ \text {au} ) ( astronomical unit ) subtends an angle of 1 second of arc.

Therefore, 1 parsec is equal to –

1 \ \text {parsec} = 3.08 \times 10^{16} \ m = 3.26 Light years.

### Practical Units for Area

(1) Barn –

It is a practical unit used for measuring very small area such as nuclear cross sections etc.

1 \ \text {barn} = 1 \times 10^{-28} \ m^2

(2) Acre –

It is a practical unit used for measuring very large area.

1 \ \text {acre} = 4047 \ m^2

(3) Hectare –

It is a practical unit also used for measuring very large area.

1 \ \text {hectare} = 1 \times 10^{4} \ m^2

### Practical Units for Mass

(1) Tonne –

1 \ \text {tonne} = 1 \times 10^{3} \ kg

It is also called metric ton.

(2) Chandra Shekhar limit –

1 \ \text {CSL} = 1.4 \times \text {Mass of the sun}

\text {CSL} is the largest practical unit of mass.

(3) Atomic mass unit –

It is the practical unit for measuring very small masses. It is defined as the mass equivalent to \left ( \frac {1}{12} \right ) part of the mass of one carbon atom.

1 \ \text {amu} = 1.66 \times 10^{-27} \ kg

The mass of a proton or a neutron is of the order of ( 1 \text {amu} ) or ( 1 \ au ) .

### Practical Units for Pressure

(1) Bar –

1 \ \text {bar} = 1 \ \text {atm} ( Atmospheric pressure )

Or, \quad 1 \ \text {bar} = 1 \times 10^{5} \ N \ m^2 = 10^{5} \ Pa (Pascal)

(2) Torr –

1 \ \text {torr} = 1 \ \text {mm of mercury ( Hg ) column}

Also, \quad 1 \ \text {atm} = 1 \text {bar} = 760 \ \text {mm of Hg} [katex] = 760 \ \text {torr}