Introduction To Physics [Unit,Measurement And Dimension]

What is Physics?

Physics is the branch of science which deal with the study of nature and its laws. It also concerned with properties of matter and energy and their interaction. From the day to day observation and experiment of new phenomenon, scientists discover the rules that are operating in nature.

The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.

Matter and Energy:

Various components are available in the nature such as Air, Water, Soil, Stone, Iron, copper, milk, etc. are known as Matter.

Element- Hydrogen (H), Oxygen (O), Iron (Fe) etc.

Compound- Water (H₂O), Salt, Hydrochloric acid (HCl) etc.

Mixture- Air, Milk etc.

Ability of doing work is known as Energy. It is found in various form. For example (1) mechanical energy, (2) thermal energy, (3) chemical energy, (4) light energy, (5) sound energy, (6) magnetic energy, (7) electric energy, (8) atomic energy.

We will learn more about work and energy in later chapter.

According to Classical physics, nature has two entity (i) Matter, (ii) Energy.

Both matter and energy neither create nor destroy, it can converted from one form to another. These are known as Law of conservation Matter and Law of conservation Energy.

But in Modern science, according to Theory of relativity Matter can converted into Energy and vice versa. It concluded that, there is one conservation law (Law of conservation of mass-energy).

Measurement, Unit, Dimension:

Objects around us has several properties, such as color, taste, smell, mass, volume, length etc. Some of them can be observed by our senses, these are qualitative description. On the other hand some properties, like mass, length, volume, etc. required qualitative as well as quantitative description, and these properties are called Physical Quantity. To compare the physical quantities, it involves measurement. To measure a physical quantity we need some standard unit of that quantity. A man is heavier than a baby but exactly how many time? This question can be easily answered if we have chosen a standard mass calling it unit mass. If the man is 100 times the unit mass and the baby 5 times, we know that the man is 20 times heavier than the baby.

Therefore, value of physical quantity = 'number' 'unit'

Fundamental and derived units:

There are a large number of physical quantities which are measured and every quantity needs a definition of unit. So, it is difficult to describe different definition for every quantities. However, not all the quantities are independent of each other. 

Quantities which are independent of other quantities are known as fundamental Quantities and there unit are known as fundamental units. It is also called Base units. And all the other quantities expressed in term of the fundamental quantities are known as derived Quantities and there units are called derived units.

Systems of unit:

Three systems of unit are mainly used around the world. Those are followings-
1. Centimeter-gram-second (CGS system)
2. Foot-pound-second (FPS system)
3. Meter-kilogram-second (MKS system)[SI Unit]

Table 1.1: Unit, Symbol, of some Quantities in different systems:

Dimension:

All the derived quantity can be related with base quantity .When a quantity is expressed in terms of the base quantities, it is written as a product of different powers of the base quantities. The exponent of a base quantity that enters into the expression, is called the dimension of quantity in that base.

                   Velocity =Length/time

Thus, the dimension of velocity are 1 in length and -1 in time. The dimension of other base quantity is Zero.

Uses of Dimension:

1. Homogeneity of dimension in an equation:
   It means dimension of all the terms of the equation are same.
Example- s = ut + ½ at²

[s]   =     [ut]       +    [½ at²]

[s] = L; [ut] = LT^-1 T = L; [½ at²] = LT^-2 T² = L

Dimension of all the terms are same (e.g. 1 in L)

Therefore, this equation is correct as far as dimensions are concerned.

Limitation of the method: 

s = ut + ½ at² and s = ut +at² both are dimensionally correct, in actual first equation is correct. Dimension does not depend on magnitude, therefore first equation is dimensionally correct. Thus, a dimensionally correct equation need not be actually correct but a dimensionally wrong equation must be wrong.

2. Conversion of Units:

Dimensions can be useful for converting unit from one system of unit to another system of unit.

Conversion of Unit from MKS (SI) To (CGS): 

3. Deducing Relation among the physical Quantities:

We want to find the relationship between the time period of simple pendulum and mass of bob, gravity and length of string.

                 t = k l^a m^b g^c ------------- (1)

Where k is dimensionless constant 

Take the dimension on both sides,

                T = L^a M^b (LT^-2)^c = L^(a+b) M^b T^-2c 

Since the dimensions on both sides must be identical,

We have

                     a + c = 0; b = 0; -2c =1

We get,    a =1/2; b =0 and c = -1/2

Putting these values in equation (1)

We get,                   t = k √ (l/g)

Solved Exercises Question Of H C Verma: Chapter 1

Previous year’s chapter-wise questions and solutions of introduction to physics [Unit, Measurement & Dimension]: Click Here                                

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