Measurements, Units and Dimensions Formula Class 11 PDF Download

Units and Measurements is one of the most important chapters in Class 11 Physics because it builds the foundation for the entire subject. Before learning motion, force, energy, electricity, magnetism, or modern physics, students must understand how physical quantities are measured, written, compared, and analyzed.

This chapter explains fundamental units, derived units, dimensional formulas, dimensional analysis, significant figures, errors in measurement, accuracy, precision, vernier caliper, screw gauge, and the principle of homogeneity of dimensions.

For quick revision, students often search for a Measurements, Units and Dimensions Formula Class 11 PDF Download so that they can revise all formulas offline before school exams, JEE, NEET, and other competitive tests.

What are Units and Measurements in Physics?

In physics, every measurable quantity is called a physical quantity. Examples include length, mass, time, velocity, force, pressure, energy, and temperature.

A physical quantity is written as:

Physical Quantity = Numerical Value × Unit

For example:

Length = 5 m

Here, 5 is the numerical value and m is the unit of length.

A unit is a standard quantity used to measure a physical quantity. Without units, a numerical value has no complete physical meaning. For example, saying “the distance is 10” is incomplete. It may be 10 m, 10 km, or 10 cm.

Also Check: CBSE Class 11 Physics Formulas

Types of Physical Quantities

Physical quantities are mainly divided into two categories:

1. Fundamental Quantities

Fundamental quantities are independent quantities that cannot be expressed in terms of other physical quantities. They form the base of the measurement system.

Examples:

2. Derived Quantities

Derived quantities are obtained by combining two or more fundamental quantities.

Examples:

SI Base Units for Class 11 Physics

The International System of Units is known as the SI system. It is the most widely accepted system of measurement in physics.

In older terminology, plane angle and solid angle were sometimes called supplementary quantities. Their units are:

Common SI Prefixes Used in Class 11 Physics

SI prefixes are used to express very large or very small quantities conveniently.

Example:

1 km = 10³ m
1 cm = 10⁻² m
1 mm = 10⁻³ m
1 μm = 10⁻⁶ m

What is Dimensional Formula in Physics Class 11?

A dimensional formula is an expression that shows how a physical quantity depends on fundamental quantities such as mass, length, time, electric current, temperature, amount of substance, and luminous intensity.

The basic symbols used in dimensional formulas are:

For example:

Speed = Distance / Time

So,

Speed = [L] / [T] = [LT⁻¹]

Therefore, the dimensional formula of speed is:

[M⁰L¹T⁻¹]

Usually, powers with zero are omitted, so it is written as:

[LT⁻¹]

Dimensional Formula List of Important Physical Quantities Class 11

Below is a high-value dimensional formula table for quick revision. Students should learn these formulas because they are frequently asked in school exams, JEE, NEET, and other entrance exams.

How to Find the Dimensional Formula of a Physical Quantity

To find the dimensional formula of any physical quantity, follow these steps:

Step 1: Write the formula

For example, force is given by:

Force = Mass × Acceleration

Step 2: Write the dimensions of each quantity

Mass = [M]
Acceleration = [LT⁻²]

Step 3: Substitute and simplify

Force = [M] × [LT⁻²]

Therefore:

Force = [MLT⁻²]

So, the dimensional formula of force is [MLT⁻²].

Principle of Homogeneity of Dimensions Class 11

The principle of homogeneity of dimensions states that only physical quantities having the same dimensions can be added, subtracted, or compared.

In any correct physical equation, the dimensions of all terms on the left-hand side must be equal to the dimensions of all terms on the right-hand side.

Example:

v = u + at

Here,

v = velocity = [LT⁻¹]
u = velocity = [LT⁻¹]
a = acceleration = [LT⁻²]
t = time = [T]

So,

at = [LT⁻²] × [T] = [LT⁻¹]

Therefore:

v = u + at
[LT⁻¹] = [LT⁻¹] + [LT⁻¹]

Since all terms have the same dimensions, the equation is dimensionally correct.

Applications of Dimensional Analysis

Dimensional analysis is a very useful tool in Class 11 Physics. It is used to check formulas, derive relationships, and convert units.

1. To Check the Correctness of a Formula

A formula is dimensionally correct if the dimensions on both sides are the same.

Example:

s = ut + ½at²

Dimensions of s = [L]

Dimensions of ut = [LT⁻¹] × [T] = [L]

Dimensions of at² = [LT⁻²] × [T²] = [L]

Since all terms have the dimension [L], the equation is dimensionally correct.

2. To Derive Relations Between Physical Quantities

Suppose the time period of a simple pendulum depends on length l and acceleration due to gravity g.

Let:

T ∝ lᵃgᵇ

Writing dimensions:

[T] = [L]ᵃ [LT⁻²]ᵇ

[T] = [Lᵃ⁺ᵇ T⁻²ᵇ]

Comparing powers:

For time:
1 = -2b
b = -1/2

For length:
0 = a + b
a = 1/2

Therefore:

T ∝ l¹ᐟ² g⁻¹ᐟ²

So,

T ∝ √(l/g)

3. To Convert Units

Dimensional analysis also helps convert a physical quantity from one system of units to another.

For example, if the dimensions of a quantity are known, its numerical value can be converted by comparing the units of mass, length, and time in different systems.

Limitations of Dimensional Analysis

Dimensional analysis is useful, but it has some limitations.

1. It cannot find dimensionless constants such as 2, ½, π, or numerical coefficients.
2. It cannot derive formulas involving trigonometric, logarithmic, or exponential functions.
3. It cannot distinguish between physical quantities having the same dimensions, such as work and torque.
4. It cannot tell whether a formula is completely correct if both sides have the same dimensions.
5. It is difficult to apply when a physical quantity depends on more variables than the number of fundamental dimensions involved.

Example:

Work and torque both have the dimensional formula:

[ML²T⁻²]

But work is a scalar quantity, while torque is a vector quantity. Dimensional analysis cannot identify this difference.

Error Analysis Class 11 Physics Formulas

No measurement is perfectly accurate. A small difference between the measured value and the true value is called an error.

Error analysis is important because it tells us how reliable a measurement is.

Types of Errors

1. Systematic Error

Systematic errors occur due to faulty instruments, incorrect calibration, or wrong experimental methods.

Examples:

• Zero error in a vernier caliper
• Incorrectly calibrated thermometer
• Faulty measuring scale

2. Random Error

Random errors occur due to unpredictable changes during measurement.

Examples:

• Variation in repeated readings
• Small changes in environmental conditions
• Human reaction time errors

3. Gross Error

Gross errors occur due to careless mistakes.

Examples:

• Wrong reading of scale
• Incorrect recording of data
• Calculation mistake

Important Error Formulas for Class 11 Physics

1. Absolute Error

If a₁, a₂, a₃, ... an are measured values and amean is the mean value, then absolute error is:

Δa₁ = |a₁ − amean|
Δa₂ = |a₂ − amean|
Δa₃ = |a₃ − amean|

2. Mean Absolute Error

Mean absolute error is given by:

Δamean = (Δa₁ + Δa₂ + Δa₃ + ... + Δan) / n

3. Relative Error

Relative error is:

Relative Error = Mean Absolute Error / Mean Value

Δa / a

4. Percentage Error

Percentage Error = Relative Error × 100

Percentage Error = (Δa / a) × 100%

5. Error in Sum or Difference

If:

Z = A + B
or
Z = A − B

Then maximum absolute error is:

ΔZ = ΔA + ΔB

6. Error in Product or Division

If:

Z = AB
or
Z = A / B

Then:

ΔZ / Z = ΔA / A + ΔB / B

7. Error in Power

If:

Z = Aⁿ

Then:

ΔZ / Z = n × ΔA / A

Example:

If Z = A², then:

ΔZ / Z = 2 × ΔA / A

Significant Figures Rules Class 11 Physics

Significant figures are the meaningful digits in a measured quantity. They show the precision of a measurement.

Rules of Significant Figures

1. All non-zero digits are significant.
   Example: 245 has 3 significant figures.
2. Zeros between non-zero digits are significant.
   Example: 1005 has 4 significant figures.
3. Leading zeros are not significant.
   Example: 0.0045 has 2 significant figures.
4. Trailing zeros after a decimal point are significant.
   Example: 2.500 has 4 significant figures.
5. Trailing zeros without a decimal point may or may not be significant.
   Example: 1500 can have 2, 3, or 4 significant figures depending on how it is written.

Significant Figures in Addition and Subtraction

In addition or subtraction, the final answer should have the same number of decimal places as the quantity with the least number of decimal places.

Example:

12.11 + 18.0 + 1.013 = 31.123

The least number of decimal places is 1, so the answer is:

31.1

Significant Figures in Multiplication and Division

In multiplication or division, the final answer should have the same number of significant figures as the quantity with the least number of significant figures.

Example:

2.5 × 3.42 = 8.55

Here, 2.5 has 2 significant figures and 3.42 has 3 significant figures.

So, the final answer should have 2 significant figures:

8.6

Accuracy and Precision Class 11 Physics

Accuracy and precision are important terms in measurement.

Accuracy

Accuracy refers to how close a measured value is to the true or actual value.

Example:

If the actual length of an object is 10.00 cm and a student measures it as 9.98 cm, the measurement is highly accurate.

Precision

Precision refers to how close repeated measurements are to each other.

Example:

If repeated measurements are 9.81 cm, 9.82 cm, and 9.81 cm, they are precise because they are close to each other.

Difference Between Accuracy and Precision

Least Count of Vernier Caliper and Screw Gauge Formulas

Vernier caliper and screw gauge are important measuring instruments in Class 11 Physics practicals.

Vernier Caliper Least Count Formula

Least Count of Vernier Caliper:

LC = Value of 1 Main Scale Division − Value of 1 Vernier Scale Division

Another common formula is:

LC = Value of 1 Main Scale Division / Number of Vernier Scale Divisions

Vernier caliper is used to measure:

• Length of small objects
• Internal diameter
• External diameter
• Depth of a vessel

Screw Gauge Least Count Formula

Least Count of Screw Gauge:

LC = Pitch / Number of divisions on circular scale

Where:

Pitch = Distance moved by the screw in one complete rotation

Screw gauge is used to measure:

• Diameter of a thin wire
• Thickness of a sheet
• Radius of small spherical objects

Important Units and Dimensions Formulas Class 11

Here is a quick formula sheet for revision.

Units and Measurements is a foundational chapter of Class 11 Physics. It helps students understand how physical quantities are measured, represented, and analyzed. Topics like dimensional formulas, error analysis, significant figures, SI units, vernier caliper, and screw gauge are important for school exams as well as competitive exams like JEE and NEET.

Students should revise the dimensional formula table, practice error-based questions, and understand the principle of homogeneity of dimensions clearly. For fast revision, download the Measurements, Units and Dimensions Formula Class 11 PDF and use it as a quick reference before exams.