UNIT AND DIMENSIONS

1. DEFINITION OF PHYSICS AND PHYSICAL QUANTITIES

1.1         DEFINITION OF PHYSICS AND PHYSICAL QUANTITIES

Physics: Physics is the branch of science, which deals with the study of nature and properties of matter and energy. The subject matter of physics includes heat, light, sound, electricity, magnetism and the structure of atoms.

For designing a law of physics, a scientific method is followed which includes the verifications with experiments. The physics, attempts are made to measure the quantities with the best accuracy. Thus, Physics can also be defined as science of measurement.

Applied Physics is the application of the Physics to help human beings and solving their problem, it is usually considered as a bridge or a connection between Physics & Engineering.

Physical Quantities: All quantities in terms of which laws of physics can be expressed and which can be measured are called Physical Quantities.

For example; Distance, Speed, Mass, Force etc.

2. UNIT

1.2  UNITS: FUNDAMENTAL AND DERIVED UNITS

Measurement: In our daily life, we need to express and compare the magnitude of different quantities; this can be done only by measuring them.

Measurement is the comparison of an unknown physical quantity with a known fixed physical quantity.

Unit: The known fixed physical quantity is called unit. OR

The quantity used as standard for measurement is called unit.

For example, when we say that length of the class room is 8 metre. We compare the length of class room with standard quantity of length called metre.

Length of class room = 8 metre

Q = UN

Physical Quantity = Numerical value × unit Q = Physical Quantity

n = Numerical value u = Standard unit

e.g. Mass of stool = 15 kg Mass = Physical quantity 15 = Numerical value Kg = Standard unit

Means mass of stool is 15 times of known quantity i.e. Kg.

Characteristics of Standard Unit: A unit selected for measuring a physical quantity should have the following properties

(i)  It should be well defined i.e. its concept should be clear.

(ii) It should not change with change in physical conditions like temperature, pressure, stress etc..

(iii) It should be suitable in size; neither too large nor too small.

(iv) It should not change with place or time.

(v) It should be reproducible.

(vi) It should be internationally accepted.

Classification of Units: Units can be classified into two categories.

1. Fundamental

2. Derived

Fundamental Quantity: The quantity which is independent of other physical quantities. In mechanics, mass, length and time are called fundamental quantities. Units of these fundamental physical quantities are called Fundamental units.

e.g. Fundamental Physical Quantity       Fundamental unit 

       Mass                                                     Kg, Gram, Pound

       Length                                                  Metre, Centimetre, Foot

       Time                                                      Second

Derived Quantity: The quantity which is derived from the fundamental quantities e.g. area is a derived quantity.

Area   = Length x Breadth

= Length x Length

= (Length)² 

Speed =Distance /Time

=Length / Time

The units for derived quantities are called Derived Units.

1.2.1 Table of Fundamental Units

1.2.2Table of Supplementary unit

3. SYSTEMS OF UNITS:

1.3 SYSTEMS OF UNITS: CGS, FPS, MKS, SI

For measurement of physical quantities, the following systems are commonly used:-

(i) F.P.S system: In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.

(ii) C.G.S system: In this system, the unit of length is centimeter, the unit of mass is gram and the unit of time is second.

(iii) M.K.S: In this system, the unit of length is metre, unit of mass is kg and the unit of time is second.

(iv) S.I System: This system is an improved and extended version of M.K.S system of units. It is called international system of unit.

 With the development of science & technology, the three fundamental quantities like mass, length & time were not sufficient as many other quantities like electric current, heat etc. were introduced.

Therefore, more fundamental units in addition to the units of mass, length and time are required.

Thus, MKS system was modified with addition of four other fundamental quantities and two supplementary quantities.

Advantage of S.I. system:

(i)  It is coherent system of unit i.e. the derived units of a physical quantities are easily obtained by multiplication or division of fundamental units.

(ii) It is a rational system of units i.e. it uses only one unit for one physical quantity. e.g. It uses Joule (J) as unit for all types of energies (heat, light, mechanical).

(iii) It is a metric system of units i.e. it’s multiples & submultiples can be expressed in power of 10.

4. DIMENSION

1.4 DIMENSIONS

Dimensions: The powers, to which the fundamental units of mass, length and time written as M, L and T are raised, which include their nature and not their magnitude.

For example,                Area = Length x Breadth

= [ L¹] × [L¹] = [L²] = [M⁰L²T⁰]

Power (0,2,0) of fundamental units are called dimensions of area in mass, length and time respectively.

e.g.      Density = mass/volume

= [M]/[L³]

= [ M¹L^-3T⁰]

5. DIMENSIONAL FORMULAR

1.5 DIMENSIONAL FORMULAE

Dimensional Formula: An expression along with the power of mass, length & time which indicates how physical quantity depends upon fundamental physical quantity.

e.g.          Speed = Distance/Time

= [L¹]/[T¹] =[M⁰L¹T^-1]

It tells us that speed depends upon L & T. It does not depend upon M.

1.5.1 Dimensional Equation: An equation obtained by equating the physical quantity with its dimensional formula is called a dimensional equation.

The dimensional equation of area, density & velocity are given as under- Area = [M⁰L²T⁰]

Dimensional formula SI& CGS unit of Physical Quantities

Assignment

Instructions: This Assignment is to be done and submitted on or before 13th October, 2025.

1.  Into how many categories is physical quantity classified based on dimensional analysis, explain? 

2. Derive the dimensional formula of following Quantity & write down their dimensions.

(i)   Density  

(ii) Power

(iii) Co-efficient of viscosity  

(iv) Angle

3. Explain which of the following pair of physical quantities have the same dimension:

 (i) Work &Power (ii) Stress & Pressure (iii) Momentum &Impulse

6. VECTORS AND SCALARS

Scalar Quantities: 

Scalar quantities are those quantities which have only magnitude but no direction.

Examples: Mass, length, density, volume, energy, temperature, electric charge, current, electric potential etc.

Vector Quantities: 

Vector quantities are those quantities which have both magnitude as well as direction.

Examples: Displacement, velocity, acceleration, force, electric intensity, magnetic intensity etc.