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Class 11 Physics Revision Notes for Chapter 2 – Units and Measurement
Class 11 Physics Chapter 2 Notes provide a thorough understanding of all measurement types, units, dimensions and errors of measurement. A physical quantity must be measured in order to determine how many standard measurements of that physical quantity are present in the thing being measured. The standard international units that are employed globally for an accurate representation of any quantity are thoroughly described in these notes. Since CBSE Class 11 Physics Chapter 2 Notes are prepared by subjectmatter experts, they will help students in gaining conceptual clarity of the chapter.
Units:
An internationally recognised standard for measuring amounts might be referred to as a unit.
 A numerical quantity has been measured together with a specific unit.
 Fundamental units are those used for base quantities (such as length, mass, etc.).
 The units that result from the combining of basic units are known as derived units.
 A System of Units is made up of both Fundamental and Derived Units.
 Système Internationale d’Unites, also known as SI, is the name given to an internationally recognised system of units. The General Conference on Weights and Measures was produced and advocated for it in 1971.
 The list of the seven base units mentioned by SI is presented in the table below.
Additionally, there are two units. The steradian (sr) and radian (rad), respectively, are units for planar angles (units for solid angles). There is no dimension for either of these.
Base Quantity  Name  Symbol 
Length  Metre  m 
Mass  Kilogram  kg 
Time  Second  s 
Electric Current  Ampere  A 
Thermodynamic Temperature  Kelvin  K 
Amount of Substance  Mole  mol 
Luminous Intensity  Candela  cd 
Special Length units:
Unit Name  Unit Symbol  Value in metres 
fermi  f  1015m 
angstrom  Å  1010 m 
Astronomical unit (average distance of the sun from the earth)  AU  1.496 x 1011m 
Light year  ly  9.46 x 1011m 
parsec  pc  3.08 x 1016m 
Measurement of Mass:
Mass is measured in kilogrammes (kg), however atoms and molecules are measured in unified atomic mass units (u). One unit is equal to onetwelfth of the mass of an isotope of carbon12, which includes the mass of electrons (1.66 1027 kg). In addition to using balances for regular weights, the mass of planets is measured using gravitational methods, and the mass of atomic particles is measured using a mass spectrograph (the radius of the trajectory will depend on the mass of the charged particle, which is moving in a constant electric and magnetic field.).
Range of Mass:
Some of them are:
OBJECT  MASS (kg) 
Electron  1030 
Proton  1027 
Red blood cell  1013 
Dust particle  109 
Raindrop  106 
Moon  1023 
Earth  1025 
Sun  1030 
Human  102 
Measurement of Time:
A clock has been used to determine the passage of time. The Cesium or Atomic clock is now used as a standard for the atomic standard of time.
 In a Cesium clock, the transition between two hyperfine levels of a caesium133 atom equals 9,192,631,770 radiation vibrations per second.
 The oscillation of the Cesium atom, which is equivalent to the vibrations of the quartz crystal and balance wheel in a conventional wristwatch will operate the caesium clock.
 The four atomic clocks maintain the nation’s standard time and frequency. The National Physical Laboratory (NPL), New Delhi, will keep a Cesium clock that will keep Indian standard time.
 Caesium clocks will be 100 percent accurate, with an uncertainty of just 1 part in 1013, meaning that no more than 3 seconds will be gained or lost in a year.
Range of Time:
Few of them include:
EVENT  TIME INTERVAL 
Period of xrays  1019 
Period of light wave  1015 
Period of radio wave  106 
Wink of an eye  101 
Period of sound wave  103 
Rotation of earth  105 
Revolution of earth  107 
Age of Universe  1017 
Accuracy and Precision of Instruments:
 Any uncertainty that results from the calculation of a measuring instrument can be referred to as an error. This can be categorised as either random or systematic.
 The resolution of the measured value to the true value can be thought of as a measurement of accuracy.
 Precision is the resolution of several measurements of the same quantity made under the same circumstances.
 When the true value of a certain length is 3.678 cm and two instruments with different resolutions are employed, 1 (less precise) and 2 (more precise) decimal places in the same order have been used up till now. When comparing two length measurements, the first will have greater accuracy but less precision whereas the second will measure the length as 3.38.
Types of Errors Systematic Errors:
Systematic Errors might be either positive or negative. The subsequent types are as follows:
 Instrumental errors result from inaccurate calibration or poor instrument design. A few instances of instrument errors are zero inaccuracy on a weighing scale and worn offscale.
 Errors in experimental techniques occur when the technique is incorrect (for instance, measuring a person’s body temperature by placing a thermometer under their armpit results in a lower reading than the actual temperature) because of environmental factors like temperature, wind and humidity.
 Personal errors are defined as errors that occur due to human negligence, improper setting or taking down an incorrect reading.
Random Errors:
Errors that occur at random in terms of sign and size are referred to as random errors. These errors occur as a result of unpredictably changing experimental settings, including temperature, power supply, mechanical vibrations, human error, etc.
Least Count Error:
The smallest value that can be measured with a measuring device is referred to as its least count. The least countrelated error on/in an instrument is known as the least count error.
By using equipment with increased precision/resolution and by using improved experimental methodologies, least count errors can be reduced (take several readings of measurement and then calculate a mean).
Errors in a Series of Measurements
 Absolute error is the size of the discrepancy between the actual value of the quantity and the absolute error of the measurement, which is the specific measurement value. The symbol for it is  Δ a (or Mod of Delta a). Although, Δ a may be negative, the mod value will always be positive. Each error will be as follows:
Δ a1=ameana1
Δ a2=ameana2………………..
Δ an=ameanan
 The arithmetic mean of all absolute errors can be used to describe the mean absolute error. It has been referred to as Δ amean
Δ amean= Δ a1+ Δ a2+ Δ a3+….+ Δ an
 The mean absolute error divided by the average value of the quantity being measured is known as the relative error.
Relative Error = Δ amean/amean
 The relative error represented as a percentage is known as percentage error. It is denoted by δ a
δ a= (Δ amean/amean ) × 100
Combinations of Errors
When a quantity depends on two or more other variables, the sum of the mistakes in the dependent and independent quantities can be used to anticipate and determine the errors in the dependent quantity. There are several methods for doing this.
Criteria  Sum or Difference  Product  Raised to Power 
Resultant value Z  Z = A±B  Z = AB  Z = Ak 
Result with error  Z ± ΔZ = (A ± ΔA) + (B ± ΔB)  Z ± ΔZ = (A ± ΔA) (B ± ΔB)  Z ± ΔZ = (A ± ΔA)k 
Resultant error range  ± ΔZ = ± ΔA ± ΔB  ΔZ Z= ΔAA±ΔBB  
Maximum error  ±ΔZ = ±ΔA + ΔB  ΔZ Z= ΔAA+ΔBB  ΔZ Z=k ΔAA 
Error  Sum of absolute  Sum of relative  K multiplied by relative error 
Significant Figures
Every measurement results in a number that contains both certain and reliable digits.
Significant digits or significant figures are reliable digits that are multiplied by the first uncertain digit. This is a representation of measurement precision, which depends on the minimal number of measurementrelated instruments.
One example is the 1.62 s period of oscillation of a pendulum. Here, 1 and 6 will be the trustworthy options, while 2 is unsure. There will therefore be three significant figures in the measured value.
Rules for the Determination of Number of Significant Figures
 Every digit that is not zero will have meaning.
 All zeros between two nonzero digits will be meaningful regardless of decimal position.
 For a number less than 1, zeros placed before nonzero digits and after the decimal are not regarded as meaningful. If there is a zero before the decimal place, it will never matter.
 If a number has no decimal place, any trailing zeroes are meaningless.
 If a number has a decimal place, the trailing zeroes will be important.
Cautions for Removing Ambiguities in Calculating Number of Significant Figures
The number of significant digits will not change regardless of the units used. For illustration,
4.700 m=470.0 cm
=4700 mm
The first two values in this case both have four significant digits, but the third quantity only has two.
When reporting measurements, use scientific notation. It is required to display numbers in powers of 10, for instance a × 10b, where b is an indication of magnitude. Example,
4.700 m = 4.700 × 102 cm
= 4.700 × 103 mm
= 4.700 × 103 km
The number of significant figures will be 4 in this case, as the power of 10 is irrelevant.
Infinite significant digits will result from multiplying or splitting exact numbers. For instance, radius = diameter/2. In this case, 2 can be represented as 2, 2.0, 2.00, 2.000 and so forth.
Rules for Arithmetic Operation with Significant Figures
Type  Multiplication/Division  Addition/Subtraction 
Rule  The final number must preserve the same number of significant digits as the original number with the fewest significant digits.  The final number must have the same number of decimal places as the original number with the fewest decimal places. 
Example  Density = MassVolume
Assume Mass = 4.237g and Volume = 2.51 cm3 (4 significant figures and 3 significant figures respectively) Density = 4.2372.51= 1.68804gcm3 = 1.68gcm3 (3 significant figures) 
The result of adding 436.32 (two digits after the decimal), 227.2 (one digit after the decimal), and.301 (three digits after the decimal) is 663.821. Since 227.2 is accurate to exactly 1 decimal place, the final number should be 663.8. 
Rules for Rounding off the Uncertain Digits
 The next digit is raised by 1 if the unimportant digit to be discarded is more than 5, otherwise it is reduced by 1.
 If the unimportant digit to be dropped is less than 5, the next digit is left unchanged.
 When the irrelevant digit to be eliminated is 5,
 If the preceding digit is not modified.
 If the preceding digit is raised by 1 if it is an odd number.
Rules for the Determination of Uncertainty in the Results of Arithmetic Calculations
The following procedure must be followed to determine the uncertainty:
 Summarise the original numbers with the least degree of uncertainty possible. Example uncertainty will be 0.1 for 3.2 and 0.01 for 3.22.
 Figure out these in percentage as well.
 After the calculations, the uncertainties are multiplied, divided, added and subtracted.
 To get the final uncertainty result in the uncertainty, round off the decimal place.
Rules
 The outcome must be accurate to ‘n’ significant figures or less in the event of a set of experimental data with ‘n’ significant figures (only in the case of subtraction).
 The relationship between a number’s relative inaccuracy and its value will depend both on n and on the number itself.
 In a multistep calculation, the findings in the middle step should have one significant figure more in all the measurements than the number of digits in the measurement with the least accuracy.
Dimensions of a Physical Quantity
The powers (exponents) to which basic quantities are raised in order to describe a physical quantity are referred to as its dimensions. They are represented by the square brackets surrounding the amount. The term “Dimensional Formula” refers to the formula that indicates how and which of the base quantities describe the dimensions of a physical quantity.
Dimensional Analysis
The only physical quantities that can be added and subtracted are those that have comparable dimensions. This is called as the Principle of Homogeneity of Dimensions. Dimensions can be multiplied and cancelled using standard algebraic techniques. In mathematical equations, quantities on both sides should always have the same dimensions.
Applications of Dimensional Analysis
When we examine an equation’s dimension consistency,
 Equations that are dimensionally accurate should have the same dimensions on both sides.
 A dimensionally accurate equation need not also be true in all dimensions, while a dimensionally erroneous equation will always be false. Although dimensional validity can be confirmed, the correct relationship between the physical quantities cannot be determined.
Deducing Relation among Physical Quantities
 Knowing how one physical quantity affects others (or independent variables) and taking that dependence into account when determining a relationship between physical quantities is necessary.
 This approach cannot be used to obtain dimensionless constants.
Units and Measurements Notes Physics Chapter 2 – Free Download
Topics Covered under Physics Chapter 2 Class 11 Notes
As stated in Chapter 2 Physics Class 11 Notes provided by Extramarks, the measurement of a certain physical quantity is expressed using an arbitrarily selected and widely recognised standard, or unit.
A physical quantity is equal to a number times a unit. For instance, a ladder’s length is 5.5 metres.
Here, 5.5 is a number, and the unit of length is a metre.
Fundamental or basic units are those that can be independently articulated. Fundamental units include, for instance, kilograms for mass, metres for length and seconds for time.
The units that result from combining the fundamental units are known as derived units. Examples of derived units include the units for area and density, which are m2, kg/m3 respectively are examples of derived units.
The International System of Units
The fundamental units of unit systems for length, mass, and time are:
 Centimetre, gramme, and second, or CGS,
 Foot, pound, and second, or FPS Metre,
 Kilogramme, and second, or MKS.
Parallax Method of Measurement of Large Distances
Large distances, such as those between planets and stars and the earth are measured using this technique.
Some Units of Large Distance
1 lightyear = 1 ly = 9.46 × 1015 m (the distance that light travels with a velocity of 3× 108 m s–1 in 1 year)
1 parsec = 3.08 × 1016 m (distance at which average radius of earth’s orbit subtends an angle of 1 arc second)
Errors in Measurements
(i) Systematic Errors:
 Instrumental mistakes
 a problem with the experimental methodology or process
 Personal errors
(ii) Random Errors: Errors that occur randomly as a result of unpredictably changing experimental conditions.
 Least Count Error: a measurement error related to the instrument’s resolution.
 Absolute Error: amean = (a1 +a2 +a3 +…+an )/n
∆a = amean – measured value
 Mean Absolute Error: ∆amean = (∆a1 +∆a2 +∆a3 +…+ ∆an )/n
 Relative Error : ∆amean/ amean
 Percentage Error: δa = (∆amean/ amean) × 100 %
Combination of Errors
 An error of a difference or a sum
If Z=A+ B then ∆Z =∆A + ∆B
If Z=A B then ∆Z =∆A + ∆B
 An error of a quotient or a product
If Z= A×B or Z=A/B
error in ‘Z’ = ∆Z/Z= (∆A/A) + (∆B/B)
 Error concerning a quantity that has been increased to power:
If Z = Ak, then ∆Z/Z = K (∆A/A)
Significant Figures
Arithmetic Operations with Significant Figures
For addition, subtraction, multiplication and division, the outcome has the same number of significant figures as it does for the integer with the fewest decimal places.
Rounding off the Uncertain Digits
If dropping digit < 5, then the preceding digit is left unaltered.
If dropping digit > 5, then the preceding digit is increased by 1
If dropped digit = 5 followed by nonzero digits, then the preceding digit is increased by 1
Units of Physical Quantities
Dimensions of:
 Length=L
 Mass=M
 Time= T
 Electric current=A
 Temperature=K
 Luminous intensity=cd
 Amount of substance = mol.
Physical objects are represented in terms of their base quantities using dimensional equations. For instance, speed = (distance/time)
FAQs (Frequently Asked Questions)
1. What topics are covered in Class 11 Chapter 2 of Physics?
Chapter 2 of Physics Class 11 includes the following:
 What is a unit?
 Derivative and fundamental units
 Metric system
 Propagation of Errors
2. Name the seven fundamental quantities.
The seven fundamental quantities include Temperature, Mass, Length, Time, Amount of light, Amount of Matter and Electric Current.