Units and Measurements Class 11 Physics

When measuring any physical quantity, we essentially compare it against a universally accepted reference standard. That’s called a unit. 

Now, a unit may occur in specified amounts for a given quantity, and that's the number of measure. Let's say, if you measure the length of a rod, it could be 5 metres. 5 is the number of times the unit metre comes as the measured quantity. 

A unit of measurement defines the magnitude of a quantity. It is used as a convention or standard for measuring the same quantity or amount. But it would not be used for measuring other types of quantities, as it would have different meanings.

Example of Units 

We can take the example of length or distance, whose amount we measure using the unit of a metre, centimetre, inch, or a kilometre, after a numeric value. 

Now, we won't use these same units to measure other physical properties, such as temperature or velocity. For temperature, the base unit would be Kelvin, whereas we would use a derived unit as metre per second to denote velocity, as it has both magnitude and direction.   

Types of Units

To communicate scientifically with researchers and engineers worldwide, there is a systematic organisation of these units. One can verify their findings with precision and clarity that create a universal language to communicate. 

As we go about the Units and Measurements Class 11 notes, we must be aware of the ​two main types of units that define all forms of physical quantities with dimensions. These are now standardised as SI Units, which we will discuss in the later section below. 

1. Base or Fundamental Units: They are independent or standalone units. They are used for other forms of measurements or other types of quantities. Common examples of base units would be the metre for length, the second for time, and so on. 
2. Derived Units: These are formed from combining two or three base units of different quantities, by using mathematical operations or physics laws. For instance, we would use the derived unit of velocity as metre per second using length divided by time. In the similar way, we would denote pressure in Pascals and use the derived unit by quantifying force per unit area, as kg/ (m.s^2).

Measurement systems have existed ever since human civilisations began. Records date back to the 3rd and 4th millennium BC, and some even before that.

Among the oldest and most representative units and measurements in history would be the Great Pyramids in Egypt, where the units of length measurements were cubits. At that time, a cubit was a reference point, measured as the length of the arm's elbow to the longest finger of the human body. There were different measurements of cubits. Greece and Rome also used different calculations of cubits. While there were sophisticated measurement systems such as base-60 system established in Sumeria more than 5000 years today. Then there were units of mass, necessary for trade in the ancient societies, with grain like wheat or water volume.

But all these old systems of measurement were not globally accepted. There would be variations of the same. 

The formalisation of units and measurement was seen in the European Age of Enlightenment, between the 18th and 19th centuries. This was a result of centuries of establishing mathematical foundations and discovering laws of physics. 

What is SI Unit?

The SI Unit is better known as the International System of Units (SI), or in French, Système Internationale d’Unités.  It is a decimal-based system whose units are on a power of 10, and it's the modern global standard for units and measurement that is accepted in most parts of the world today. It uses seven base units, including metre, kilogram, second, ampere, and kelvin. With these, other units are derived to maintain scientific consistency worldwide. The SI Unit is more favoured in scientific calculations than others, because it makes conversion of units convenient and simple with decimal prefixes. 

The International Bureau of Weights and Measures (BIPM) is an intergovernmental organisation that maintains the SI standards today. The International Committee for Weights and Measures (CIPM) that is run by General Conference on Weights and Measures (CPGM) together oversee the functioning of BIPM. 

Early Measurement Systems in Europe and World

• Metric System in 1799: This measurement system was based on the decimal metric system, with the metre and kilogram. It was introduced around the French Revolution in the late 1700s. 
• CGS or Centimetre-Gram-Second System in the 1870s: The CGS system used the base units of mass, length, and time. It came from mathematicians and scientists in Germany and the Great Britain, including Carl Friedrich Gauss and James Clark Maxwell, who recommend the use of base units so that they remain coherent in the then scientific community. That would be centimetre for length, gram for mass, and second for time. 
• MKS or Metre-Kilogram-Second System in Early 20th Century: The MKS system was introduced to measure more of everyday objects and to counter the CGS system, which would be more applicable to smaller sizes, distances, and objects.  The base units in the MKS system maps to metre for length, kilogram for mass, and seconds for time. 
• FPS or Foot-Pound-Second System in the UK and the USA: This system uses foot for length, pound for mass, and second for time. It has different variants for the Imperial System of the UK and for the USA Customary System.  
• SI Unit in the 1960s: This system was standardised in the 1960s, and included seven base units. The base units have been taken from the MKS system and have included a few more derived units as well.   

 

 

 

This is the list of SI Units in Class 11 Physics Chapter 1 Units and measurements notes​ In your book, you can further refer to Table 1.1. 

7 Base Quantities with Dimensions and SI Units

1. Length - The SI unit for length is the metre, symbolised by m.
2. Mass - Mass has an SI Unit of kilogram. The symbol for that is kg. 
3. Time - Time remains in seconds in the SI Unit and the other historical systems of measurement. The symbol for seconds is s.  
4. Electric - This denotes the unit for an electric current amount, and has an SI unit of Ampere (A). 
5. Thermodynamic Temperature - Kelvin is the unit for temperature, and the symbol is K. 
6. Amount of Substance  - This refers to mole as the SI Unit and uses mol for its symbol. NCERT further mentions on page 3 of this chapter on Units and Measurements that “when mole is used, the elementary entities must be specified. These entities may be atoms, molecules, ions, electrons, other particles or specified groups of such particles.”
7. Luminous Intensity - To measure how much brightness is there for a point light source, we need to look at luminous intensity. It uses the SI Unit, candela. The symbol is cd. 

2 Derived Quantities without Dimensions and with SI Units

You should know about two derived quantities under SI units without dimensions.

• Plane Angle: This angle appears on a two-dimensional plane, and the SI unit for a plane angle is Radian, symbolised as rad.
• Solid Angle: On a three-dimensional plane, we see this solid angle with the SI Unit as Steradian, with the symbol, sr. 

Every measurement cannot be too perfect. It will have some uncertainty, as there are limitations of measuring instruments and human observation. 

That’s why we have the way to use Significant figures (sig fig) that provides a systematic way to express the precision of measurements. These help us avoid false precisions in calculations. 

We have summarised the rules adopted for significant figures below. Give importance to the rules for significant figures in Class 11 Physics for your exams. You would have to correctly apply these when summing or when calculating the errors of derived quantities.   

Significant Figure Rules Class 11

Rule Type	Description	Example
Non-zero digits	Always significant	2.34 has 3 sig figs
Zeros between non-zeros	Always significant	205 has 3 sig figs
Leading zeros	Never significant	0.023 has 2 sig figs
Trailing zeros (with decimal)	Always significant	2.50 has 3 sig figs
Trailing zeros (no decimal)	Not significant	250 has 2 sig figs

Physical quantities have an intrinsic quality - dimension. 

Dimensions of physical quantities can describe the fundamental nature of an object in how it exists in shape and size. They are independent of the units, as units are arbitrary or have no meaning if there isn't a dimension.  

There are seven basic quantities to express dimensions. 

• Length [L] 
• Mass [M] 
• Time [T] 
• Electric current [A] 
• Temperature [K] 
• Luminous intensity [cd]
• Amount of substance [mol]

You can say this is the dimensional framework that is universal in showing how physical quantities exist. 

In any physical quantity, dimensions are the powers to which the base units are raised. This helps in getting one unit or better understood as to see how those dimensions would exist with the base quantities.   

When revising Physics Class 11 Notes Chapter 1, give special importance to this section.  

What are Dimensional Formulas?

Dimensional formulas in physics are expressions which help us see the base quantities and their dimensions. 

Important Dimensional Formulas in Class 11 Physics

Physical Quantity	Dimensional Formula	Example
Area	[L²]	m²
Volume	[L³]	m³
Speed	[LT⁻¹]	m/s
Acceleration	[LT⁻²]	m/s²
Force	[MLT⁻²]	Newton
Energy	[ML²T⁻²]	Joule

What are Dimensional Equations?

Dimensional equations tell is if the dimensional formula shown as the power of the quantities based on their units is correct or not. The basic quantities or dimensions are the mass, length, and time, and using these we can check if the dimensional equations are correct or not.

For that, we must learn another principle. 

Principle of Homogeneity of Dimensions

This principle says that the left and right-hand sides of any equation must have the same kind of dimensions. 

When there are functions, such as trigonometric or logarithmic, we must look at the quantities inside of the function. The quantities must not have dimensions so that the maths and physics remain consistent.

 

This first chapter of Physics Class 11 has some additional and related formulas you may want to look at when preparing for competitive tests, such as JEE Mains. These come in applied learning. 

Error Analysis Formulas in Units and Measurement

 

• Absolute Error Formula: This one will tell how much each measurement differs from the average. 

$\mathrm{\Delta a}{i}_{}=|a_{\mathrm{mean}}-a_i|$

Here, a_mean is the average of all values, and a_i is one measurement. 

• Mean Absolute Error Formula: This formula calculates the average of all the absolute errors that occur in a set of measurements. 

$\mathrm{\Delta a}{\mathrm{mean}}_{}=\frac{\mathrm{\Delta a}1+\mathrm{\Delta a}2+\cdots +\mathrm{\Delta a}n}{n}$

• Relative Error Formula: This is the ratio of the mean absolute error to the mean value of the quantity to measure. 

$\text{Relative Error}=\frac{{\mathrm{\Delta a}}_{\mathrm{mean}}}{a_{\mathrm{mean}}}$

• Percentage Error Formula: This is another way to write the relative error formula in percentage form. 

  Percentage error = Relative error x 100