Types of Units

Generally we can use any convenient unit to measure a physical quantity depending on how much magnitude we are measuring or in which system of units we want to measure it.

What kind of unit we should use?

The unit i) must be accepted internationally.

ii) Should be reproducible.

iii) Should be invariable.

iv) Should be easily available.

v) Should be consistent.

vi) Should be large, if the physical quantity to be measured is a big quantity.

Ex: To measure larger lengths we use units like Km, mt etc, to measure large magnitude of time we use units like hour , day ,week, month , year etc.

vii) Should be small if the physical quantity to be measured is small.

Ex: To measure small time we use units like millisecond, microsecond etc

To measure small lengths we use units like millimeter, centimeter etc.

Types of physical Quantities.:

We can broadly divide the physical quantities in to two types i)Fundamental Physical quantities ii)Derived physical quantities.

Fundamental physical quantities: A physical quantity which can exist independently is called Fundamental physical quantity.

Ex: Length, mass and time etc.

Derived physical quantities: A physical quantity which can not exist independently is called derived physical quantity. (Or) A physical quantity which is dependent or derived from any other physical quantity is called derived physical quantity.

Ex : Area, volume, density, speed, acceleration, force, energy etc.

Like the physical quantities we can divide the units in to two types. I)Fundamental units ii)derived units.

Fundamental units : The units of fundamental physical quantities are called fundamental units, (or) The units which are independent or can not derived from any other unit is called fundamental unit.

Ex:­ Every unit of length is fundamental unit (irrespective of the system to which it belongs);millimeter, centimeter, meter, kilometer etc.

­ Every unit of time is a fundamental unit. microsecond, millisecond, second, minute, hour, day etc are units of time.All these units are fundamental units.

Derived units: The units of derived physical quantities are called derived units. Units of area, volume, speed, density, energy etc are derived units.

Ex: ­ Every unit of speed is a derived unit ; m/sec, cm/sec, km/hr etc.

­ Every unit of density is a derived unit; kg/m³, gr/cm³ etc.

­ Every unit of acceleration is a derived unit; m/sec², cm/sec², km/hr² etc.

System of Units: To measure the fundamental physical quantities Length,Mass and Time we have three systems of units, they are i) C.G.S system(metric system) ii) F.P.S system (British system)   and iii) M.K.S system. In all these three systems only three physical quantities mass,length and time are considered to be fundamental quantities.

But, in system International (S.I) system there are seven fundamental physical quantities. Which are i)Mass ii)Length iii) Time iv)Electric current v) Thermo dynamic temperature vi) Luminous intensity vii) Quantity of substance.

In addition to the above seven fundamental quantities two more supplementary physical quantities were add.They are i) Plane angle ii)Solid angle.

Multiple choice questions – Units&Dimensions.

1 . 1KWH is  unit of

Ans : 1.Time 2. Power 3. Energy 4. Stress

2. Unit of  Intensity of magnetic induction field  is

Ans : 1.N/Am  2. Tesla   3.Wb/$m^{2}$    4. All above

3. Which of the following has no units?

Ans : 1. Thermal capacity    2. Magnetic susceptibility 3. Angular acceleration 4. Moment of a magnet

4.Which one of the following units is a fundamental unit?

Ans : 1. watt   2. joule/sec  3. ampere 4. newton

5. $10^5$ Fermi is equal to

Ans : 1. 1 meter      2. 100  micron      3.   1angstrom unit 4. 1 mm

6. kg m/sec is the unit of

Ans : 1. Impulse 2. Angular acceleration 3 . Capacity of condenser   4. Acceleration.

7. candela is the unit of

Ans : 1. Magnetic flux   2. Intensity of electric field    3. Luminous intensity 4. Charge

8. If  10 newton = X dynes, the value of  x is

Ans : 1.$10^6$ 2.$10^4$ 3.$10^8$          4.$10^3$

9. 1 KWh is equal to

Ans : 1. 360 J    2. 1800 J   3.$1800\times10^5$J 4. $360\times10^5$J

10. Which of the following is a common unit of a physical quantity in M.K.S & S.I systems.

Ans : 1. ampere  2.kelvin   3. mole  4. joule/sec

Units & Dimensions Q&A

1. What is a physical quantity?

Ans : Any quantity which is measurable is called physical quantity.

2. Explain the term Fundamental Physical quantity.

Ans: The physical quantity which is independent or which can not be derived from any other physical quantity is called fundamental physical quantity. EX: Mass, Length and Time.

3.Explain the term Derived physical quantity.Give examples.

Ans :The physical quantity which is dependent on other physical quantity or which is derived from other physical quantity is called derived physical quantity. Ex : Area, Electric charge, Magnetic field strength, power etc.

4.How many fundamental quantities are there in C.G.S; F.P.S and M.K.S systems? What are they?

Ans : There are 3 fundamentals quantities in C.G.S; F.P.S and M.K.S systems, they are mass, length and time.

5.How many fundamental quantities are there in S.I systems? What are they?

Ans : In S.I system 7 fundamental quantities are there,they are i) Mass ii)Length iii)Time iv)Electric current v)Intensity of light vi) Thermodynamic temperature vii) Quantity of matter.

6.How many supplementary quantities are there in S.I system? What are they?

Ans : In S.I system there are 2 supplementary quantities, they are i) Plane Angle ii) Solid Angle.

7. What are the units of length in C.G.S ; F.P.S and M.K.S systems.

Ans : The units of length  are cm,foot and meter respectively in C.G.S ; F.P.S and M.K.S systems .

8. what are the units of fundamental quantities in S.I system?

Ans : Mass → kg ; Length → m ; Time → sec ; Electric current → Amp Thermodynamic temperature → kelvin ;

Intensity of light → candela ; Quantity of matter → mole .

9.what are the units of supplementary quantities in S.I system?

Ans : Plane angle → radian ; Solid angle → steradian .

10. Name the physical quantities whose dimensional formula is $M^0L^1T^0$ ?

Ans : The physical quantities are i)Distance or length ii) displacement iii)wave length

11. Name the physical quantities whose dimensional formula is $M^0L^1T^{-1}$ ?

Ans : The physical quantities are i) speed ii) velocity

12.Name the physical quantities whose dimensional formula is $M^1L^2T^{-2}K^{-1}$ ?

Ans : The physical quantities are i)Thermal capacity ii) Entropy

13. Name the physical quantities whose dimensional formula is $M^1L^1T^{-1}$ ?

Ans : The physical quantities are i)Momentum ii) impulse .

14.Name the physical quantities whose dimensional formula is $M^1L^1T^{-2}$ ?

Ans : The physical quantities are i)force ii ) Tension iii) weight .

15.Name the physical quantities whose dimensional formula is $M^1L^2T^{-2}$ ?

Ans : The physical quantities are i) Work ii) Energy iii) Heat iv)Moment of force Iv) Torque .

16.Name the physical quantities whose dimensional formula is $M^1L^{-1}T^{-2}$?

Ans : The physical quantities are i) pressure ii ) stress iii) Young’s modulus iv) Rigidity modulus v) Bulk modulus .

17.Name the physical quantities whose dimensional formula is $M^0L^0T^{-1}$ ?

Ans : The physical quantities are i) frequency ii) Decay constant iii)Angular velocity .

18 . Name the physical quantities whose dimensional formula is $M^1L^2T^{-1}$ ?

Ans : The physical quantities are i )angular momentum ii )Plank constant .

19. Name the physical quantities whose dimensional formula is $M^1L^0T^{-2}$ ?

Ans : The physical quantities are i )Force constant ii )surface tension .

20. Which physical quantity has negative dimensions in mass ?

Ans : Gravitational constant (G) .

21. State few constants which have dimensions ?

Ans : i) Plnak’s constant (h) ii)Velocity of light in vacuum (c) iii)Permeability of free space ($\mu_0$) iv) Permittivity of free space ($\epsilon_0$) v)Universal gravitational constant (G) vi) Universal gas constant (R)

vii)Boltzmann constant (k) .

22 .which physical quantities have the unit henry ?

Ans : self Inductance and Mutual Inductance have the unit henry .

23. What are the dimensions of  electric conductivity in mass , length and current.

Ans : Electric conductivity has -1,-3 and 2 dimensions  in mass,length and current respectively.

24. What is the unit of electric conductivity in C.G.S and S.I systems?

Ans : It has no unit in C.G.S system ; its unit in S.I system is Siemen/meter or S/m.

25.What are the uses of Dimensional methods?

Ans : To convert units from one system to another. ii )To check the correctness of equations connecting physical quantities iii )To derive the expressions connecting physical quantities.

26. Which is the physical quantity whose S.I unit is Am ?

Ans: Magnetic pole strength.

27. V/m or N/Coulomb are the units of ……. Physical quantity.

Ans : These are the units of Electric field strength.

28.Name five physical quantities which neither have dimensions nor units.

Ans : Refractive Index , specific gravity,susceptibility,dielectric constant,  coefficient of friction.

29. If  V = Xt+Y ; V is the velocity , t is time.What are the dimensional formulas of X and Y ?

Ans : According to principle of homogeneity of dimensions, the dimensions  of M,L and T in every term should be same.

Therefore $M^0L^1T^{-1}$ = X $M^0L^0T^1$ → X = $\frac{M^0L^1T^{-1}}{ M^0L^0T^1}$ ; X → $L^1T^{-2}$ and Y→ $L^1T^{-1}$

30.Which physical quantities does not possess dimensions in mass ?

Ans :Area,volume, velocity, acceleration,angular displacement, angular velocity, angular acceleration.

Special Units.

1. Length:

• Micron($\mu$ )= $10^{-6}$m = $10^{-4}$ cm
• Angstrom (A) = $10^{-10}$m = $10^{-8}$cm
• Fermi = $10^{-15}$m = $10^{-13}$cm
• Astronomical Unit (A.U) = (1.5) $10^{11}$m  = (1.5) $10^{13}$cm;                                                                                                      What is 1 A.U?                                                                                                                                                                                                                                   Ans: 1 A.U(Astronomical Unit) is the distance between Earth and Sun. 1A.U=(1.496) $10^{8}$km.
• X ray unit (X.U) = $10^{-13}$m (wave length of X-Rays)
• Light year = Distance traveled by light in one year= $9.5\times 10^{15}$m =$9.5\times 10^{12}$km
• parsec = 3.26 light years = $3.1\times 10^{16}$m
• 1 mile = 1.609 km = 8 furlongs = 1760 yards = 5280 feet
• 1 agate(typography) = 0.07 inch = 1.8 centimeter
• 1 angstrom = 0.0000001 mm = 0.000000004 inch
• 1 cable’s length = 720 feet = 219.46 meters
• 1 chain (engineer’s) = 100 feet = 30.48 meters
• 1 chain (Gunter’s or surveyor’s) = 66 feet = 20.12 meters
• 1 cubit = 18 inches = 45.72 centimeter
• 1 degree (geographical) = 69.05 miles = 111.12 kilometers
• 1 decametre = 10 meters = 32.81 feet
• 1 fathom = 6 feet = 1.83 meters
• 1 hand = 4 inches = 10.16 centimeters
• 1 league = 3 miles = 4.83 kilometers
• 1 link (engineer’s) = 1 foot = 0.31 meter
• 1 link (gunter’s or surveyor’s ) = 7.92 inches = 10.16 centimeters
• 1 perch or pole = 16.5 feet = 5 meters
• 1 point (typography ) = 0.1 inch = 0.35 millimeter

2.Time :

• Solar day def: The time taken by earth to complete one rotation about its own axis with respect to sun is called solar day. (Avarage value for all the days of one year is Mean solar day).
• Siderial day : It is 4.1min shorter than Mean solar day .
• siderial year :365.26 Mean solar day  d ) Solar year = 365.24 Mean solar day
• Lear year = The year in which February month has 29 days is called leap year.It is divisible by 4.
• Lunar month :Time taken by moon to complete one rotation around earth is lunar month = 27.3 days.

3. Mass :

• Atomic mass Unit ( a.m.u) : = $\frac{1}{12}$of mass of  $C_{12}$  atom =$\frac{1}{12}\times\frac{12}{N}$ = $\frac{1}{6.023\times10^{23}}$ gr = $1.67\times10^{-24}$gr = $1.67\times10^{-27}$kg.
• 1 assay ton = 29.167 grams = 1.03 ounces
• 1 carat = 200 milligrams = 3.09 grains
• 1 decigram = 100 milligrams = 1.54 grains
• 1 decagram = 10 grams = 0.35 ounce
• 1 pound = 0.45 kilograms

4.Pressure :

• Atmosphere =760 mmHg = $76\times13.6\times980$ dyne/$cm^{2}$ = $1.013\times10^6$ dyne/$cm^{2}$ = $1.013\times10^5 N/m^{2}$or pa.
• Bar = 750 mmHg = $75\times13.6\times980$ dyne/$cm^{2}$=$10^6$ dyne/$cm^{2}$ = $10^5 N/m^{2}$or pa.
• Torr =1 mm Hg =$0.1\times13.6\times980$ dyne/$cm^{2}$=1333 dyne/$cm^{2}$=133N/$m^{2}$ or pa.

5.Area :

• Barn: this is unit of area,it is used to measure cross section of nuclei.
• Barn =$10^{-28}$ $m^{2}$
• 1 acre = 4047 sq meters = 4840 sq yards = 43560 sq ft
• 1 are = 100 square meters = 1076.39 sq feet
• 1 square(building) = 100 sq feet = 9.29 sq meters
• 1 sq link = 62.73 sq inches = 404.69 sq cm
• 1 township = 36 sq miles = 93.24 sq kms

6. Wind Speeds :

• light wind = 7 miles/hr
• light breeze = 11 miles/hr
• gentle breeze = 16 miles/hr
• moderate breeze = 20 miles/hr
• fresh breeze = 25 miles/hr
• strong breeze = 30 miles/hr
• moderate gale = 35 miles/hr
• fresh gale =45 miles/hr
• strong gale = 50 miles/hr
• whole gale = 60 miles/hr
• storm = 70 miles/hr
• hurricane = 80 miles/hr

7.Horse Power : It is the British Unit of power =746 w.

8.Special units of derived Physical Quantities:

 S.NO Physical Quantity C.G.S Unit S.I Unit 1 Force Dyne Newton 2 Work , Energy Erg Joule 3 Power Watt 4 Pressure Pascal 5

Multiples,sub multiples of units.

Multiples and sub multiples of Units in S.I system :

Depending upon the magnitudes of physical quantities we measure, we have to use different multiplication factors suitable for that particular case.Here let us see some widely used multiplication factors.

 Multiplication Factor Prefix symbol $10^{-1}$ deci d $10^{-2}$ centi c $10^{-3}$ milli m $10^{-6}$ micro $\mu$ $10^{-9}$ nano n $10^{-12}$ pico p $10^{-15}$ femto f $10^{1}$ deca da $10^{2}$ hecta h $10^{3}$ kilo K $10^{6}$ mega M $10^{9}$ giga G $10^{12}$ tera T $10^{15}$ peta P

Units in different systems.

Generally we can use any convenient unit to measure a physical quantity depending on how much magnitude we are measuring or in which system of units we want to measure it.

What kind of unit we should use?

The unit i) must be accepted internationally.

ii) Should be reproducible.

iii) Should be invariable.

iv) Should be easily available.

v) Should be consistent.

vi) Should be large, if the physical quantity to be measured is a big quantity.

Ex: To measure larger lengths we use units like Km, mt etc, to measure large magnitude of time we use units like hour , day ,week, month , year etc.

vii) Should be small if the physical quantity to be measured is small.

Ex: To measure small time we use units like millisecond, microsecond etc

To measure small lengths we use units like millimeter, centimeter etc.

Types of physical Quantities.:

We can broadly divide the physical quantities in to two types i)Fundamental Physical quantities ii)Derived physical quantities.

Fundamental physical quantities: A physical quantity which can exist independently is called Fundamental physical quantity.

Ex: Length, mass and time etc.

Derived physical quantities: A physical quantity which can not exist independently is called derived physical quantity. (Or) A physical quantity which is dependent or derived from any other physical quantity is called derived physical quantity.

Ex : Area, volume, density, speed, acceleration, force, energy etc.

Like the physical quantities we can divide the units in to two types. I)Fundamental units ii)derived units.

Fundamental units : The units of fundamental physical quantities are called fundamental units, (or) The units which are independent or can not derived from any other unit is called fundamental unit.

Ex:­Every unit of length is fundamental unit (irrespective of the system to which it belongs);millimeter, centimeter, meter, kilometer etc.

­ Every unit of time is a fundamental physical quantity ; microsecond, millisecond, second, minute, hour, day etc.

Derived units: The units of derived physical quantities are called derived units. Units of area, volume, speed, density, energy etc are derived units.

Ex: ­ Every unit of speed is a derived unit ; m/sec, cm/sec, km/hr etc.

­ Every unit of density is a derived unit; kg/m³, gr/cm³ etc.

­ Every unit of acceleration is a derived unit; m/sec², cm/sec², km/hr² etc.

Systems of units: To measure the fundamental physical quantities Length, Mass and time we have three systems of units, they are i) C.G.S System (Metric system)ii)F.P.S System (British system) and iii)M.K.S System. In all these three systems only three physical quantities length, mass and time are considered to be fundamental quantities.

But, in systems International (S.I) system there are seven fundamental physical quantities. Which are i)Length ii)Mass iii)Time iv)Electric current v)Thermo dynamic temperature vi)Luminous intensity vii)Quantity of substance.

In addition to these two more quantities were added as supplementary physical quantities. They are i)Plane angle ii)Solid angle.

Systems,Fundamental physical quantities and their units:In
C.G.S system: Length (centimeter); Mass (gram); Time (second).

F.P.S system :Length (foot);Mass(pound);Time (second).

M.K.S system: Length (meter); Mass (kilogram); Time (second).

S.I System:Length (meter); Mass (kilogram); Time (second); Electric current (ampere); Thermodynamic temperature (kelvin); Intensity of light (candela); Quantity of matter (mole). The units of suplimentary quantities are Plane angle( radian); Solid angle(Steradian).

What are Units

Metric system

In my previous post, I explained with example how to solve the In problems in physics. To solve problems and to under stand the basics of the Physics it is very important to know what is a physical quantity, types of physical quantities, what is a unit, what are the units of different physical quantities, types of units, symbols of units.

There is one and only branch of science which measures a physical quantity, that branch of science is “Physics”. Measurements have an important role not only in physics but also in every branch of science and everywhere in our day-to-day life.

To measure physical quantities we need units. Let’s try to understand necessity of measurements and units of measurement in Physics.

The information about a physical quantity, by description of its external properties like color, taste etc is incomplete with out knowing its temperature, size (dimensions), which depends on measurement

, i.e. with out measurements it is impossible to know about the external properties of any object. So, it becomes necessary to measure it.

To measure a physical quantity we require a unit. Different physical quantities will have different units.

What is unit? A standard reference of the same physical quantity is essential to measure any physical quantity. That standard which we use to measure a physical quantity is called unit.

Let me put it this way, if we want to measure length of a table, we have to select a standard length (length of our hand), and by comparing the table’s length with the standard length we can measure the length of the table. If the table is 3.5 times that of standard length, i.e. length of our hand then we can write the result as “length of table = 3.5 times the length of our hand. In this example length of hand is taken as standard length to measure the table’s length.

Like that we can define any convenient standard or unit to measure a physical quantity.

But, if we choose standards as in the above example which are not consistent, and can not be reproduced then  errors and confusion in measurements will creep in. To avoid such confusion, instead of taking any undefined reference as a standard, well-defined and universal standards are used. Such a reference taken a standard is generally called a well defined unit or unit. Measurement of every physical quantity will have two parts a number (n) followed by a unit (u).

There fore n u = constant.

Ex: If the length of a table is 1.2 meters.In this measurement number n= 1.2 and unit is meter.

→ length (L)= $n_1u_1$ = 1.2 meters

→ length (L)= )= $n_2u_2$ = 120 centimeters

→ length (L)= $n_3u_3$ = 1200 millimeters

From the above data we can understand that

i)we can measure a physical quantity in different units.what ever may be the unit it’s value is same.

→ L =$n_1u_1$ = $n_2u_2$=$n_3u_3$

If theunit cosen is smaller, the multiple number will be greater.

$u_1$>$u_2$>$u_3$ = $n_1$ <$n_2$<$n_3$

iii)The units(u) of a physical quantity will be reciprocal to the multiple (n)

nu=constant$\Rightarrow$ $n_1u_1$=$n_2u_2$

u$\propto\frac{1}{n}$ or n$\propto\frac{1}{u}$

$\frac{n_1}{ n_2}$= $\frac{u_2}{ u_1}$