CBSE Class 11 Physics Revision Notes for Units and Measurements: Based on CBSE Syllabus 2023-24

Class 11 Units and Measurements Short Notes: Revision notes or short notes are best for recalling all important concepts and topics quickly at the time of an exam. Download here revision notes by subject experts for 2023-24 exam preparations.

Units and Measurements Class 11 Revision Notes: The Units and Measurements chapter in CBSE Class 11 deals with the concepts of physical quantities, units, systems of units, and measurements. The chapter is an important part of the class 11 Physics syllabus because it lays the foundation for understanding the concepts of measurement and dimensional analysis. With the help of short notes presented in this article, students will be able to revise all the concepts in just a few minutes. These notes have been prepared according to the new CBSE syllabus for Class 11 Physics. Subject experts have created and reviewed the revision notes to provide students with the most accurate and reliable study material. Therefore, these notes are best to revise the chapter during exam preparations. You can download the notes in PDF as well.

Also Read:

CBSE Class 11 Physics Syllabus 2023-24

CBSE Class 11 Physics Deleted Syllabus 2023-24

Revision Notes for CBSE Class 11 Physics Chapter 1, Units and Measurements

Physical quantities:

All those quantities which can be measured directly or indirectly are called physical quantities.

Unit:

A unit is an internationally accepted standard for measurements of quantities.

Fundamental units are all those units which are independent of any other unit.

Derived units are all those units which are obtained by multiplying and/or dividing one or more fundamental units.

Systems of Units:

It encompasses a complete set of units which is used for measuring all kinds of physical quantities. They are CGS, FPS, MKS and SI unit systems.

SI Units – Fundamental Units

Supplementary Units

Significant figures:

Significant figures in the measured value of a physical quantity is the sum of the reliable digits and the first uncertain digit.

Significant figures in the product, quotient, sum or difference of two numbers should be reported with same number of decimal places as that of the number with minimum number of decimal places.

The example gives the following rules :

• All the non-zero digits are significant.
• All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all.
• If the number is less than 1, the zero(s)on the right of decimal point but to the left of the first non-zero digit are not significant. [In 0.00 2308, the underlined zeroes are not significant].
• The terminal or trailing zero(s) in a number without a decimal point are nonsignificant.

[Thus 123 m = 12300 cm = 123000 mm has three significant figures, the trailing zero(s) being not significant.]

• The trailing zero(s) in a number with a decimal point are significant.

[The numbers 3.500 or 0.06900 have four significant figures each.]

Important Note:

• Change of units should not change number of significant digits.
• Use scientific notation to report measurements. Numbers should be expressed in powers of 10 like a x 10^bwhere b is called order of magnitude.
• Multiplying or dividing exact numbers can have infinite number of significant digits.

Rules for Arithmetic Operation with Significant Figures

1.Multiplication or Division

Final result should retain as many significant figures as are there in the original number with the least significant figures.

2.Addition or Subtraction

Final result should retain as many decimal places as are there in the number with the least decimal places.

Rounding off the Uncertain Digits

1.Preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5, and is left unchanged if the latter is less than 5.

Example (i):

Number  – 6.137 (if the insignificant digit to be dropped is more than 5)

Result – 6.14

Example (ii):

Number  – 6.132 (if the insignificant digit to be dropped is less than 5)

Result – 6.13

2.For insignificant digit to be dropped is equal to 5, there are two cases:

a.If preceding digit is even, it is left unchanged.

b.If preceding digit is odd, it is raised by 1.

Example (i):

Number  – 6.125 (if preceding digit is even)

Result – 6.12

Example (ii):

Number  – 6.135 (if preceding digit is odd)

Result – 6.14

Rules for Determining the Uncertainty in the Results of Arithmetic Calculations

1.For a set experimental data of ‘n’ significant figures, the result will be valid to ‘n’ significant figures or less (only in case of subtraction). Example 12.9 – 7.06 = 5.84 or 5.8

2.The relative error of a value of number specified to significant figures depends not only on n but also on the number itself.

3.Intermediate results in multi-step computation should be calculated to one more significant

figure in every measurement than the number of digits in the least precise measurement.

Dimensions: The dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity.

Dimensional equations are the equations, which represent the dimensions of a physical quantity in terms of the base quantities.

For example,

• Dimensional equation for volume, [V] = [M⁰L¹T^-1]
• Dimensional equation for speed, [v] = [M⁰LT^-1]
• Dimensional equation for force, [F]= [M¹L¹T^-2]
• Dimensional equation for mass density, [ρ] = [ML³T⁰]

Principle of homogeneity of dimensions: A physical equation will be correct if the dimensions of all the terms occurring on both sides of the equation are the same.

Dimensional analysis:

• Only those physical quantities which have same dimensions can be added and subtracted. This is called principle of homogeneity of dimensions.
• Dimensions can be multiplied and cancelled like normal algebraic methods.
• In mathematical equations, quantities on both sides must always have same dimensions.
• Arguments of special functions like trigonometric, logarithmic and ratio of similar physical quantities are dimensionless.
• Equations are uncertain to the extent of dimensionless quantities.

Applications of dimensional analysis:

• To check the correctness of a physical equation.
• To derive the relationship between different physical quantities.
• To convert a physical quantity from one system of units to other.

Limitations of dimensional analysis:

• Dimensionless constants cannot be obtained by this method.
• It fails when the physical quantity is the sum or difference of two or more quantities
• It does not distinguish between the physical quantities having same dimensions.
• It fails to derive the relationships which involve trigonometric, logarithmic or exponential functions

Also Read:

NCERT Book for Class 11 Physics (Revised Book)
NCERT Solutions for Class 11 Physics (All Chapters)