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JEE Physics

Class 11 Chapter 1

Class 11 Physics Chapter 1: Units and Measurements

Units and Measurements is the first chapter of Class 11 Physics and serves as the foundation for understanding every concept in Physics. It introduces physical quantities, SI units, dimensions, dimensional analysis, significant figures, and measurement errors. Mastering these concepts is essential for performing accurate calculations and solving numerical problems in JEE Main, JEE Advanced, NEET, and CBSE Board examinations.

At ALLEN, Chapter 1: Units and Measurements smart study notes are carefully prepared by expert faculty to help students build strong conceptual clarity and revise efficiently before examinations. This study materials include concise theory, important formulas, solved examples, previous years' question trends, and exam-oriented tips that strengthen accuracy and problem-solving skills. Whether you are preparing for CBSE Board exams, JEE Main, or JEE Advanced, these notes provide a structured and effective revision resource to boost your confidence and performance.

1.0Chapter Snapshot

Parameter	Details
Difficulty Level	Easy to Moderate
JEE Main Weightage	Moderate (Generally 1 Question)
JEE Advanced Weightage	Moderate (1–2 Questions)
Key Concepts Covered	Physical Quantities, SI Units, Dimensions, Dimensional Analysis, Significant Figures, Errors in Measurement

2.0Chapter 1 Smart Study Material by ALLEN Experts: Download PDFs

Continue your preparation by exploring these resources after completing Units and Measurements. These study materials will help reinforce concepts, improve numerical accuracy, and strengthen exam readiness.

Practice Resources

Resource	Access
Chapter Mock Test Paper
Chapter Mock Test Solution
Practice Paper with Solution

Test your Knowledge

question 1 of 5

Which of the following system of units is not based on units of mass, length and time alone?

1.SI

2.MKS

3.FPS

4.CGS

Must-Revise Concepts

Experimental Skills

Experimental Skills PYQ With Solutions

Fundamental And Derived Unit

Fundamental and Derived Units

Need For Measurement

Physical World and Measurement

Scope and Methodology of Physics

Types of motion measurement

Unit and Dimension

Units and Dimensions PYQ With Solutions

Units and Measurement

Units and Measurements are essential for expressing physical quantities in a standardized way. The International System of Units (SI) includes base units like meter (m) for length, kilogram (kg) for mass, and second (s) for time. Measurements can involve scalar quantities (e.g., mass) or vector quantities (e.g., velocity). Dimensional analysis helps in converting and verifying units. Accuracy is how close a measurement is to the true value, while precision is the consistency of repeated measurements. Errors can be systematic (due to equipment or methods) or random (due to unpredictable factors).

1.0Fundamental Forces And Its Range

1. Gravitational Force: Gravitational force is the weakest force in nature. It is the force of mutual attraction between two objects due to their masses. This force is universal in nature.

2. Electromagnetic Force: Electromagnetic force is the force between charged particles. When charges are in motion, they generate magnetic fields, which in turn exert a force on other moving charges. Since electric and magnetic effects are generally interrelated, this interaction is referred to as the electromagnetic force.

3. Strong Nuclear Force: The strong nuclear force holds protons and neutrons together in the nucleus. Without this attractive force, the nucleus would be unstable due to the electric repulsion between protons. The strong nuclear force is the strongest of all fundamental forces. It is charge independent.It is equal for protons and neutrons.Its range is extremely small, of the order of nuclear dimensions (10-15 10^-15 m).

4. Weak Nuclear Force: The weak nuclear force is involved only in specific nuclear processes, such as the β-decay of a nucleus. During β-decay, the nucleus emits an electron and an uncharged particle known as the antineutrino. While the weak nuclear force is not as weak as gravity, it is significantly weaker than the strong nuclear force. Its range is extremely small, on the order of 10-16 10^{-16} meters.

Range of Fundamental Forces

Gravitational Force→Infinite
Electromagnetic Force→ Infinite
Strong Nuclear Force→ Short (Nuclear Size: $1 0^{- 15}$ M)
Weak Nuclear Force→Very Short ( $1 0^{- 16}$ M)

Relative Strength

2.0Physical Quantities

Physical quantities are those quantities used to describe the laws of physics that can be measured.

Classification On Basis Of Directional Properties

Fundamental or Base Quantities: The quantity that does not depend upon other quantities for its complete definition.

(1) Mass

(2) Length

(3) Time

(4) Temperature

(5) Current

(6) Luminous Intensity

(7) Amount of Substance

Derived Quantities:The quantity that can be described in terms of the fundamental quantity.

(1) Area

(2) Force

(3) Density

1.0Dimensions and Dimensional Formula

Dimensions: It is a physical quantity are the powers to which the base quantity are raised to express that quantity.

Dimensional Formula:

The expressions that represent how and which of the base quantities are included in that quantity.

NOTE: It is expressed by placing the symbols for the base quantities with the correct powers inside square brackets.

$M a ss \to [M^{1} L^{0} T^{0}]$

$M o m e n t u m \to [M^{1} L^{1} T^{- 1}]$

$F orce \to [M^{1} L^{1} T^{- 2}]$

Dimensional Equation:The equation formed by equating a physical quantity to its dimensional formula is known as a dimensional equation.

$M a ss \to [M^{1} L^{0} T^{0}]$

$L e n g t h \to [M^{0} L^{1} T^{0}]$

$T im e \to [M^{0} L^{0} T^{1}]$

$T e m p er a t u re \to [M^{0} L^{0} T^{0} K^{1}]$

$C u rre n t \to [M^{0} L^{0} T^{0} A^{1}]$

$Lu min o u s I n t e n s i t y \to [M^{0} L^{0} T^{0} C d^{1}]$

$A m o u n t o f S u b s t an ce \to [M^{0} L^{0} T^{0} mo l^{1}]$

Dimensions of differential coefficients and integrals

$[\frac{d ^{n} y}{d x ^{n}}] = [\frac{y}{x ^{n}}] an d [\int y d x] = [y x]$

2.0Rule of Dimensions

Only SAME physical quantities can be added or subtracted.

A + B = C – D

Dimensionless Quantities

Dimensionless Quantities are:

• Ratio of physical quantities with same dimensions.

• All mathematical constants.

• All standard mathematical functions and their inputs (exponential, logarithmic, trigonometric & inverse trigonometric).

3.0Conversion between System of Units

Magnitude = numeric value (n) × unit (u) = constant

$n_{1} u_{1} = n_{2} u_{2}$

$n_{2} = n_{1} (\frac{u _{1}}{u _{2}})$

So, if a quantity is represented by [MaLbTc] then:

$n_{2} = n_{1} (\frac{M _{1}}{M _{2}})^{a} (\frac{L _{1}}{L _{2}})^{b} (\frac{T _{1}}{T _{2}})^{c}$

$n_{1} = numerical value in I system$

$n_{2} = numerical value in II system$

$M_{1} = unit of mass in I system$

$M_{2} = unit of mass in II system$

$L_{1} = unit of Length in I system$

$L_{2} = unit of Length in II system$

$T_{1} = unit of time in I system$

$T_{2} = unit of time in II system$

4.0Law of Homogeneity and Dimensions of Unknown Quantities

Applications of Dimensional Formula

To verify the dimensional accuracy of a given physical equation:

If in a given relation, terms on both the sides have the same dimensions, then the relation is dimensionally correct. This is known as the Principle of Homogeneity of Dimensions.

To verify the dimensional correctness of a given physical relationship:

If in a given relation, the terms on both the sides have the same dimensions, then the relation is dimensionally correct. This is known as the principle of homogeneity of dimensions.

Relation among Physical Quantities

To derive relationships between different physical quantities: Using the same principle of homogeneity of dimensions new relations among physical quantities can be derived if the dependent quantities are known.

5.0Limitations of Dimensional Analysis

1.In Mechanics the formula for a physical quantity depending on more than three physical quantities cannot be derived. It can only be checked.

2. This method can be used only if the dependency is of multiplication type.

3. The formulae containing exponential, trigonometrical and logarithmic functions cannot be derived using this method.

4. Formulae containing more than one term which are added or subtracted like $s = u t + \frac{1}{2} a t^{2}$ also cannot be derived.

5. The relation derived from this method gives no information about the dimensionless constants.

6. If dimensions are given, physical quantities may not be unique as many physical quantities have the same dimensions.

7. It gives no information whether a physical quantity is a scalar or a vector.

6.0Significant Figures, Rounding off and Order of Magnitude

Significant Figures or Digits

Significant figures (SF) in a measurement are the figures or digits that are known with certainty plus one that is uncertain (i.e. Last digit).

The significant figures in a measured value of a physical quantity indicate the number of digits that are considered reliable. The greater the number of significant figures in a measurement, the higher its accuracy, and vice versa.

Rules to find out the number of significant figures

I Rule : All the non-zero digits are significant e.g. 1984 has 4 SF.

II Rule : All the zeros between two non-zero digits are significant. e.g. 10806 has 5 SF.

III Rule : All the zeros to the left of the first non-zero digit are not significant. e.g.00108 has 3 SF.

IV Rule : If a number is less than 1, the zeros to the right of the decimals point but to the left of the first non-zero digits are not considered significant. For example, the number 0.002308 has 4 significant figures.

V Rule : The trailing zeros (zeros to the right of the last non-zero digit) in a number with a decimal point are significant. e.g. 01.080 has 4 SF.

VI Rule : The trailing zeros in a number without a decimal point may not be significant e.g. 010100 has 3 SF.

VII Rule : When the number is expressed in exponential form, the exponential term does not affect the number of S.F. For example, in

$x = 12.3 = 1.23 \times 1 0^{1} = 0.123 \times 1 0^{2} = 0.0123 \times 1 0^{3} = 123 \times 1 0^{-} 1$ Each term has 3 SF only.

Rules for arithmetical operations with significant figures

I Rule :In addition or subtraction, the result should have the same no. of decimal places as the term with the fewest decimal places in the operation. For example, in the calculation 12.587−12.5=0.08712.587 - 12.5 = 0.087, the result is rounded to 0.10.1 because the second term has only one decimal place.

II Rule : In multiplication or division, the number of SF in the product or quotient is the same as the smallest number of SF in any of the factors. e.g. 2.4 × 3.65 = 8.8

Rounding off

To represent the result of any computation containing more than one uncertain digit, it is rounded off to an adequate number of significant figures.

Rules for rounding off the numbers:

I Rule : If the digit to be rounded off is more than 5, then the preceding digit is increased by one. e.g. 6.87 ≈ 6.9

II Rule : If the digit to be rounded off is less than 5, then the preceding digit is left unchanged. e.g. 3.94 ≈ 3.9

III Rule : If the digit to be rounded off is 5, then the preceding digit is increased by one if it is odd and is left unchanged if it is even. e.g. 14.35 ≈ 14.4 and 14.45 ≈ 14.4

Order of Magnitude

The order of magnitude of a quantity is the power of 10 needed to express that quantity. This power is determined after properly rounding the value of the quantity. When rounding, if the last digit is less than 5, it is ignored, while if it is 5 or greater, the digit is increased by one.

• When a number is divided by 10x (where x is the order of magnitude of the number), the result will always fall between 0.5 and 5, i.e., 0.5 ≤N/ $1 0^{x}$ < 5.

7.0Types and Representation of Errors

Errors in Measurement

Every measurement made with a measuring instrument carries some degree of uncertainty, which is referred to as an error. The error in a measurement is the difference between the true value and the measured value of a quantity.

Error = True value – Measured value

Types of Errors

1. Systematic Errors:- Systematic errors are errors with known causes, and they can be either positive or negative. Since their causes are understood, these errors can be minimised. Systematic errors can be further classified into three types:

(i) Instrumental Errors : Error due to imperfect design or calibration of the measuring instrument.

(ii) Environmental Errors : These errors result from variations in outer environmental conditions, such as temperature, pressure, humidity, dust, and vibrations.

(iii) Observational Errors : These errors occur due to faulty setup of the apparatus or Carelessness in recording observations.

2. Random Errors: These errors occurred from unknown factors, making them unpredictable and variable in both magnitude and direction. Since their exact causes are not fully understood, they cannot be entirely eliminated.

3. Gross Errors: Gross errors occur due to human mistakes or carelessness in taking readings, as well as errors in calculating or recording measurement results.

8.0Representation Of Errors

1.Absolute Error ( $Δ a$ ): The difference between the true value and an individual measured value of the quantity.

Absolute Error = True Value – Measured Value

$Δ a = a_{T} - a$

If the true value of a quantity is not given then the mean of all the measured values is taken.

$a_{m} = \frac{1}{n} \sum_{i = 0}^{n} a_{i}$

2.Mean Absolute Erroram: The arithmetic mean of all the absolute errors(magnitudes) is defined as the final or mean absolute error.

$Mean Absolute Error = (Δ a)_{m} = \frac{1}{n} \sum_{i = 0}^{n} ∣ a_{i} ∣$

3.Relative Or Fractional Error:The ratio of the mean absolute error to either the true value or the average value of the measured quantity.

$Relative Error = \frac{Mean Absolute Error}{True Value} \Rightarrow Relative Error = \frac{( Δ a ) _{m}}{a _{m}}$

4.Percentage Error: When the relative error is represented as a percentage, it is referred to as the percentage error.

$Percentage Error = Relative Error \times 100%$

$P erce n t a g e E rror = \frac{Mean Absolute Error}{True Value} \times 100%$

5. the Least Count: It is the smallest value of a physical quantity that can be calculated accurately by an instrument.

Least Count Error: This is related to the resolution of the measuring instrument.If the instrument has unknown least count the absolute error is taken to be equal to the least count unless otherwise stated.

Rule 1: - Addition or Subtraction of Quantities:

The maximum absolute error in the sum or difference of two quantities is equal to the sum of the absolute errors in each of the individual quantities.

X=A+B or X=A-B then the maximum absolute error in X is $Δ X = Δ A + Δ B$

Maximum percentage error = $\frac{Δ X}{X} \times 100%$

Result will be written as $X \mp Δ X$ ((in terms of absolute error)

$X \mp (\frac{Δ X}{X} \times 100%)$ (in terms of PercentageError)

Rule 2:Multiplication or Division of Quantities:

The maximum fractional or relative error in the product or quotient of quantities is the sum of the fractional or relative errors of the individual quantities involved.

If $X = A B or X = \frac{A}{B} then \frac{Δ X}{X} = \mp (\frac{Δ A}{A} + \frac{Δ B}{B})$

Rule 3:The maximum fractional error in a quantity raised to power n is n times the fractional error in the quantity itself

1. If $X = A^{n} t h e n \frac{Δ X}{X} = n (\frac{Δ A}{A})$

2. If $X = A^{p} B^{q} C^{r} t h e n \frac{Δ X}{X} = [p (\frac{Δ A}{A}) + q (\frac{Δ B}{B}) + r (\frac{Δ C}{C})]$

3. If $X = \frac{A ^{p} B ^{q}}{C ^{r}} t h e n \frac{Δ X}{X} = [p (\frac{Δ A}{A}) + q (\frac{Δ B}{B}) + r (\frac{Δ C}{C})]$

9.0Vernier Callipers

A measuring instrument used to measure linear dimensions, the Vernier calliper is also employed to measure the diameters of round objects using its measuring jaws. The Vernier scale, invented by French mathematician Pierre Vernier in 1631, enhances the accuracy of measurements. The primary advantage of the Vernier calliperwith the over the main scale is its ability to provide highly accurate and precise measurements.

Least Count of Vernier Callipers

Let the size of one main scale division (M.S.D.) be M units, and the size of one Vernier scale division (V.S.D.) be V units. Additionally, assume that the length of 'a' main scale divisions is equal to the length of 'b' Vernier scale divisions.

$a M = bV \Rightarrow V = \frac{a}{b} M$

∴ $M - V = M - \frac{a}{b} M = (\frac{b - a}{b}) M$

$[M \to MS D, V \to V S D]$

$L . C = M - V = (\frac{b - a}{b}) M$

Least Count(x)=Difference between MSD & VSD

10 VSD=9 MSD

1 VSD=0.9 MSD

x=1 MSD-1 VSD=1 MSD -0.9 MSD=0.1 MSD

Generally,1 MSD=1mm

x=0.1 mm

Measurement with Vernier Calliper

Reading=Main Scale Reading+Vernier Scale Reading

Reading=MSR+V S coincided with the division with MS ✕ LC

Zero Error

If the zero marking of the main scale and Vernier calliper do not coincide, necessary correction has to be made for this error which is known as zero error of the instrument.

1. Positive Zero Error :If the zero of the Vernier scale is to the right of the zero on the main scale, the zero error is considered positive. To obtain the corrected value, the zero error must always be subtracted from the reading.

Positive Zero Error Correction

READING = (Main Scale Reading) + (Vernier Scale Reading) – ZE

Positive zero error = VS Coincided division with MS × LC

2. Negative Zero Error

If the zero of the Vernier scale is to the left of the zero of the main scale the

zero error is said to be negative.

The zero error is always subtracted from the reading to get the corrected

value.

Negative Zero Error Correction

Negative zero error = –(Total VSD – VS Coincided division with MS) × LC

10.0Screw Gauge

A screw gauge is the most accurate instrument for measuring spherical or cylindrical objects. However, an intricately calibrated screw gauge can be challenging for untrained hands to use effectively. The goal of this article is to familiarize individuals with the fundamentals of using a screw gauge.

Pitch of Screw Gauge:

The pitch of the instrument is the distance between two consecutive threads of the screw which is equal to the distance moved by the screw due to one complete rotation of the cap.

Least Count of Screw Gauge

The minimum (or least) measurement (or count) of length is equal to one division on the main scale, which is equal to pitch divided by the total cap divisions.

Pitch of screw gauge = P
Number of division on circular scale = N
$Least count of screw gauge = \frac{Pitch}{Total number of divisions on circular scale}$

Length as measured by Screw Gauge

The formula for measuring the length is, L = (n × pitch) + (f × least count)

Where, n = main scale reading;f=Circular scale reading

Zero Error in Screw Gauge

If there is no object between the studs (i.e., the studs are in contact), the screw gauge should ideally show a zero reading. However, due to the presence of extra material on the studs, the gauge may give a small positive reading even when there is no object. This excess reading is referred to as zero error.

Calculation of zero error for screw gauge: -

Positive zero error = CS Coincided division with MS × LC

Negative zero error = –(Total CSD – CS Coincided division with MS) × LC

Correct reading = (Reading) – (zero error)

Calculation of zero error for screw gauge: -

11.0Spherometer

12.0Parts of Spherometer

1.Main Scale

2.Circular Scale

Pitch of screw gauge = P

Number of division on circular scale = N

Least count of Spherometer = $\frac{P}{N}$

13.0Accuracy and Precision

Accuracy: The extent of closeness between the measured value and the true value.

It refers to the capability of an instrument to measure the true or correct value. It represents how close the measured value is to the standard or true value. To achieve accuracy, it is important to take multiple measurements, as smaller readings help minimize calculation errors.

Precision: How consistent our results are, regardless of proximity to true value.

The precision of a substance refers to the closeness of two or more measurements to each other. For example, if you weigh a substance five times and obtain 4.3 kg each time, your measurements are highly precise, but this does not necessarily mean they are accurate. Precision is independent of accuracy.

Solved Examples

Q-1 Find the dimensions of unknown quantities p, q in the following:

$U = p cos (qt + \frac{π}{6})$ where, U: - Potential energy, t :- Time

Solution:

Dimensions of potential energy $[U] = [M^{1} L^{2} T^{- 2}]$

Inside cos function →dimensionless

qt→Dimensionless

$qt = [M^{0} L^{0} T^{0}]$

$q = \frac{[ M ^{0} L ^{0} T ^{0} ]}{[ T ^{1} ]} = [T^{- 1}]$

$U = p = [M^{1} L^{2} T^{- 2}]$

Q-2.Given that the time of revolution T of a satellite around the Earth depends on the universal gravitational constant G, the mass of the Earth M, and the radius of the circular orbit RR, derive an expression for T using dimensional analysis.

Solution:

$[T] \propto [G]^{a} [M]^{b} [R]^{c}$

$\Rightarrow [M^{0}] [L^{0}] [T^{1}] = [M]^{- a} [L]^{3 a} [T]^{- 2 a} \times [M]^{b} [L]^{c} = [M]^{b - a} [L]^{c + 3 a} [T]^{- 2 a}$

$[T] 1 = - 2 a \Rightarrow a = - \frac{1}{2}$

$[M] 0 = b - a \Rightarrow b = a = - \frac{1}{2}$

$[L] 0 = c + 3 a \Rightarrow c = - 3 a = \frac{3}{2}$

$[T] \propto [G]^{- 1/2} [M]^{- 1/2} [R]^{3/2} \Rightarrow T \propto \frac{R ^{3}}{GM}$

$T = 2 π \frac{R ^{3}}{GM}$

Q-3.Convert 1 newton (SI unit) into dyne (CGS unit)?

Solution:

$n_{1} u_{1} = n_{2} u_{2} \Rightarrow n_{2} = n_{1} (\frac{u _{1}}{u _{2}})$

$n_{2} = 1 [\frac{M _{1}}{M _{2}}] [\frac{L _{1}}{L _{2}}] [(\frac{T _{1}}{T _{2}})]^{- 2} = 1 [\frac{kg}{gm}] [\frac{m}{cm}] [(\frac{s}{s})]^{- 2}$

$n_{2} = 1 [\frac{1000 gm}{gm}] [\frac{100 cm}{cm}] [(\frac{s}{s})]^{- 2} = 1 0^{5}$

Q-4.If the jaws of the vernier calliper are in contact with each other, calculate the zero error of the vernier calliper, given that the Vernier Scale Division (VSD) is 3 and the least count is 0.1 mm.

Solution:

When the jaws of the vernier calliper are in contact with each other, the least count of the vernier calliper is defined as:

LC = MSD – VSD

LC = 0.1 mm

The main scale reading, MSR = 0 mm

The vernier scale reading, VSR = 3

Therefore, Zero error = MSR + VSR × LC = 0 + 3 × 0.1 = 0.3 mm

Q-5.The screw gauge has a pitch of 1 mm, and there are 100 divisions on the circular scale. When measuring the diameter of a sphere, the linear scale reads 6 divisions, while 40 divisions of the circular scale align with the reference line. Calculate the diameter of the sphere.

Solution:

Least count of the screw gauge is L.C = pitch / number of circular divisions = 1/100 = 0.01mm

Linear scale reading (LSR) = 6 × 1mm = 6mm

Circular scale reading (CSR) = 40 × 0.01mm

Diameter of the sphere = LSR + (CSR × L.C) = 6 + (40 × 0.01) = 6.4mm

Also Read:-

Need For Measurement	Vectors in Physics	Addition of Vectors
Newton’s First Law of Motion	Rotational Motion	Capacitor
Electrostatics	Magnetic Effects of Current and Magnetism	Alternating Current

1.0Learning Outcomes

After completing these Units and Measurements Revision Notes, you will be able to:

Understand the importance of physical quantities and standard units.
Differentiate between fundamental and derived physical quantities.
Apply the SI system of units correctly in numerical problems.
Write dimensional formulas of various physical quantities.
Use dimensional analysis to verify equations and derive relationships.
Apply the rules of significant figures while performing calculations.
Calculate absolute, relative, and percentage errors accurately.
Use error propagation rules for experimental measurements.
Improve accuracy and speed while solving JEE Main and JEE Advanced numerical questions.

2.05-Minute Quick Revision

If you have only 5 minutes before your exam or mock test, focus on revising these high-weightage concepts and formulas to maximize your score.

Must-Revise Concepts

Physical Quantities
Fundamental Quantities
Derived Quantities
SI System of Units
Supplementary Units
Dimensions and Dimensional Formula
Principle of Dimensional Homogeneity
Significant Figures
Accuracy and Precision
Absolute Error
Relative Error
Percentage Error
Error Propagation

Important Formula Recall

Before attempting numerical questions, quickly revise these essential formulas:

Dimensional Formula
Mean Value Formula
Absolute Error
Relative Error
Percentage Error
Error in Addition and Subtraction
Error in Multiplication and Division
Error in Powers
Significant Figures Rules
Principle of Dimensional Homogeneity

3.0High Weightage Topics

The following topics have consistently appeared in JEE Main and JEE Advanced examinations and should be given higher priority during revision.

Topic	Focus Area
Physical Quantities	Fundamental and Derived Quantities
SI Units	Base Units and Derived Units
Dimensions	Writing Dimensional Formulae
Dimensional Analysis	Verification of Equations and Derivation
Significant Figures	Rounding-off Rules
Measurement Errors	Absolute, Relative and Percentage Errors
Error Propagation	Addition, Multiplication and Powers
Accuracy & Precision	Experimental Measurements

4.0Formula Handbook

The following formulas are the most important for solving JEE Main and JEE Advanced questions from Units and Measurements.

5.0Common Mistakes & JEE Tips

Units and Measurements is a foundational chapter where students often lose marks due to incorrect unit conversions, mistakes in dimensional analysis, and improper handling of significant figures and errors. Avoiding these mistakes can significantly improve accuracy in JEE Main and JEE Advanced.

Common Mistake	Correct Approach
Mixing SI and CGS units	Always convert all quantities into SI units before solving.
Writing incorrect dimensional formulae	Memorize the dimensions of fundamental quantities and derive carefully.
Ignoring significant figures	Follow the rules of significant figures while performing calculations.
Confusing accuracy with precision	Accuracy indicates closeness to the true value, whereas precision indicates consistency of repeated measurements.
Incorrect percentage error calculation	Apply the correct formula using mean absolute error.
Using wrong error propagation rules	Use separate rules for addition, subtraction, multiplication, division, and powers.
Forgetting dimensional analysis	Verify every derived equation using the principle of dimensional homogeneity.
Ignoring units in the final answer	Always write the correct SI unit along with the numerical value.

6.0ALLEN Faculty Tips

Memorize all seven SI base units along with their symbols.
Learn the dimensional formulae of commonly used physical quantities.
Practice dimensional analysis to verify equations quickly.
Revise the rules of significant figures before attempting numerical questions.
Solve previous years' JEE questions on measurement errors and dimensional analysis.
Always check unit consistency before finalizing any numerical answer.
Avoid unnecessary rounding during intermediate calculations.
Revise error propagation formulas regularly to improve speed and accuracy.

7.0PYQ Trend Analysis

Units and Measurements is one of the most fundamental chapters in Class 11 Physics and regularly contributes conceptual as well as numerical questions in both JEE Main and JEE Advanced. Questions are generally based on dimensional analysis, SI units, significant figures, and measurement errors.

Note: The trend below is based on the analysis of previous years' JEE Main and JEE Advanced question papers. The exact number of questions may vary each year.

Concept	Questions Asked (Last 5 Years)	Average Difficulty
SI Units	2–3	Easy
Dimensions & Dimensional Formula	5–6	Easy–Moderate
Dimensional Analysis	4–5	Moderate
Significant Figures	3–4	Easy
Measurement Errors	4–5	Moderate
Error Propagation	2–3	Moderate

Most Common Question Types

Writing dimensional formulae of physical quantities.
Checking the correctness of equations using dimensional analysis.
Unit conversion between different systems of units.
Significant figures and rounding-off calculations.
Absolute, relative, and percentage error problems.
Error propagation in experimental measurements.
Assertion–Reason and concept-based MCQs on SI units and dimensions.

8.0Smart Revision Strategy

If you're short on time, revise the chapter in the following order:

Physical Quantities
SI System of Units
Fundamental and Derived Units
Dimensions and Dimensional Formulae
Principle of Dimensional Homogeneity
Significant Figures
Measurement Errors
Error Propagation
Important Formula Revision
Previous Years' Questions (PYQs)

Class 11 Physics Chapters List:- JEE & NEET Revision Notes

Chapter 1 Units and Measurements

Chapter 2 Motion in a Straight Line

Chapter 3 Motion in a Plane

Chapter 4 Laws of Motion

Chapter 5 Work, Energy and Power

Chapter 6 System of Particles and Rotational Motion

Chapter 7 Gravitation

Chapter 8 Mechanical Properties of Solids

Chapter 9 Mechanical Properties of Fluids

Chapter 10 Thermal Properties of Matter

Chapter 11 Thermodynamics

Chapter 12 Kinetic Theory

Chapter 13 Oscillations

Chapter 14 Waves

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Class 11 Physics Chapter 1: Units and Measurements

Units and Measurements is the first chapter of Class 11 Physics and serves as the foundation for understanding every concept in Physics. It introduces physical quantities, SI units, dimensions, dimensional analysis, significant figures, and measurement errors. Mastering these concepts is essential for performing accurate calculations and solving numerical problems in JEE Main, JEE Advanced, NEET, and CBSE Board examinations.

At ALLEN, Chapter 1: Units and Measurements smart study notes are carefully prepared by expert faculty to help students build strong conceptual clarity and revise efficiently before examinations. This study materials include concise theory, important formulas, solved examples, previous years' question trends, and exam-oriented tips that strengthen accuracy and problem-solving skills. Whether you are preparing for CBSE Board exams, JEE Main, or JEE Advanced, these notes provide a structured and effective revision resource to boost your confidence and performance.

1.0Chapter Snapshot

Parameter	Details
Difficulty Level	Easy to Moderate
JEE Main Weightage	Moderate (Generally 1 Question)
JEE Advanced Weightage	Moderate (1–2 Questions)
Key Concepts Covered	Physical Quantities, SI Units, Dimensions, Dimensional Analysis, Significant Figures, Errors in Measurement

2.0Chapter 1 Smart Study Material by ALLEN Experts: Download PDFs

Continue your preparation by exploring these resources after completing Units and Measurements. These study materials will help reinforce concepts, improve numerical accuracy, and strengthen exam readiness.

Practice Resources

Resource	Access
Chapter Mock Test Paper
Chapter Mock Test Solution
Practice Paper with Solution

Units and Measurement

Units and Measurements are essential for expressing physical quantities in a standardized way. The International System of Units (SI) includes base units like meter (m) for length, kilogram (kg) for mass, and second (s) for time. Measurements can involve scalar quantities (e.g., mass) or vector quantities (e.g., velocity). Dimensional analysis helps in converting and verifying units. Accuracy is how close a measurement is to the true value, while precision is the consistency of repeated measurements. Errors can be systematic (due to equipment or methods) or random (due to unpredictable factors).

1.0Fundamental Forces And Its Range

1. Gravitational Force: Gravitational force is the weakest force in nature. It is the force of mutual attraction between two objects due to their masses. This force is universal in nature.

2. Electromagnetic Force: Electromagnetic force is the force between charged particles. When charges are in motion, they generate magnetic fields, which in turn exert a force on other moving charges. Since electric and magnetic effects are generally interrelated, this interaction is referred to as the electromagnetic force.

3. Strong Nuclear Force: The strong nuclear force holds protons and neutrons together in the nucleus. Without this attractive force, the nucleus would be unstable due to the electric repulsion between protons. The strong nuclear force is the strongest of all fundamental forces. It is charge independent.It is equal for protons and neutrons.Its range is extremely small, of the order of nuclear dimensions (10-15 10^-15 m).

4. Weak Nuclear Force: The weak nuclear force is involved only in specific nuclear processes, such as the β-decay of a nucleus. During β-decay, the nucleus emits an electron and an uncharged particle known as the antineutrino. While the weak nuclear force is not as weak as gravity, it is significantly weaker than the strong nuclear force. Its range is extremely small, on the order of 10-16 10^{-16} meters.

Range of Fundamental Forces

Gravitational Force→Infinite
Electromagnetic Force→ Infinite
Strong Nuclear Force→ Short (Nuclear Size: $1 0^{- 15}$ M)
Weak Nuclear Force→Very Short ( $1 0^{- 16}$ M)

Relative Strength

2.0Physical Quantities

Physical quantities are those quantities used to describe the laws of physics that can be measured.