Unit and Measurement? – Class 9 CBSE Physics Book Summary

🔹 Introduction to Measurement

In Physics, measurement means comparing a physical quantity with a standard quantity (called a unit).

Example:
To measure the length of a table, we compare it with a standard unit like meter.

🔹 Physical Quantities

Physical quantities are those quantities which can be measured.

They are classified as:

Fundamental Quantities – Cannot be derived from others.
Examples: Length, Mass, Time, Temperature, Electric Current, Luminous Intensity, Amount of Substance.
Derived Quantities – Derived from fundamental quantities.
Examples: Speed, Area, Volume, Density, Force, etc.

🔹 Units

A unit is the standard used to measure a physical quantity.

Types of Units:

Fundamental Units – Used for fundamental quantities.
Example: Meter (m), Kilogram (kg), Second (s), Kelvin (K), Ampere (A), Mole (mol), Candela (cd)
Derived Units – Formed from fundamental units.
Example: m/s (for speed), m² (for area), kg/m³ (for density)

🔹 System of Units

Three systems used earlier:

CGS – Centimeter, Gram, Second
FPS – Foot, Pound, Second
MKS – Meter, Kilogram, Second

Modern system:

SI System (International System of Units) – Globally accepted and used.

SI Base Units:

Quantity	Unit	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Electric current	ampere	A
Luminous intensity	candela	cd
Amount of substance	mole	mol

🔹 Measurement of Length

Small lengths: Measured using vernier calipers, screw gauge (for precision).
Large distances: Measured in light-years, astronomical units (AU).
1 light-year = Distance travelled by light in 1 year.

🔹 Measurement of Mass

Measured using beam balance, electronic balance, etc.
SI unit is kilogram (kg).

🔹 Measurement of Time

Measured using clocks, watches, stopwatch, atomic clocks.
SI unit is second (s).
1 second is defined using vibrations of cesium atom.

🔹 Accuracy, Precision, and Errors

Accuracy – How close the measured value is to the actual value.
Precision – How close measured values are to each other.
Error – The difference between measured and actual value.

Types of Errors:

Systematic Errors – Due to instrument or observer mistakes.
Random Errors – Due to unpredictable variations.

Least count: Smallest value that can be measured by an instrument.

Absolute Error = |Measured value – True value|
Relative Error = (Absolute Error / True value)
Percentage Error = Relative Error × 100

🔹 Significant Figures

Digits that carry meaningful information about precision.
Rules:
1. All non-zero digits are significant.
2. Zeros between digits are significant.
3. Leading zeros are not significant.
4. Trailing zeros in decimal numbers are significant.

🔹 Scientific Notation

Used to express very large or small numbers in the form:

N × 10ⁿ,
where 1 ≤ N < 10 and n is an integer.

Example:

5000 = 5 × 10³
0.00042 = 4.2 × 10⁻⁴

🔹 Dimensional Analysis

Used to:

Convert units from one system to another.
Check correctness of formulas.
Derive formulas.

Dimensional Formula:

Represents a physical quantity in terms of basic dimensions like M (mass), L (length), T (time), etc.

Example:
Speed = distance/time → [M⁰L¹T⁻¹]

🔹 Applications of Dimensional Analysis

Checking correctness of equations.
Converting units.
Deriving new relations among physical quantities.

Here are some examples of dimensional formulas for common physical quantities in Class 9 Physics. These formulas express each quantity in terms of the base dimensions:

✅ Dimensional Formulas Examples

Physical Quantity	Formula or Definition	Dimensional Formula
Length (L)	–	[M⁰ L¹ T⁰]
Mass (m)	–	[M¹ L⁰ T⁰]
Time (t)	–	[M⁰ L⁰ T¹]
Speed / Velocity	Distance / Time	[M⁰ L¹ T⁻¹]
Acceleration	Velocity / Time	[M⁰ L¹ T⁻²]
Force	Mass × Acceleration	[M¹ L¹ T⁻²]
Work / Energy	Force × Distance	[M¹ L² T⁻²]
Power	Work / Time	[M¹ L² T⁻³]
Pressure	Force / Area	[M¹ L⁻¹ T⁻²]
Density	Mass / Volume	[M¹ L⁻³ T⁰]
Momentum	Mass × Velocity	[M¹ L¹ T⁻¹]
Kinetic Energy	(1/2)mv²	[M¹ L² T⁻²]
Potential Energy	mgh	[M¹ L² T⁻²]
Gravitational Constant (G)	F = G (m₁m₂/r²)	[M⁻¹ L³ T⁻²]
Planck’s constant (h)	E = hν	[M¹ L² T⁻¹]
Frequency	1 / Time	[M⁰ L⁰ T⁻¹]
Area	Length × Breadth	[M⁰ L² T⁰]
Volume	Length³	[M⁰ L³ T⁰]

💡 Note:

M = Mass
L = Length
T = Time

Here are some important questions based on Chapter: Units and Measurement (Class 9 CBSE Physics)—divided into Very Short, Short, and Long Answer Types, including numerical and reasoning questions.

📘 Very Short Answer Questions (1 mark)

What is the SI unit of mass?
Write the dimensional formula of speed.
Name two instruments used to measure small lengths.
Define 1 light year.
What is meant by least count of an instrument?
How many significant figures are there in 0.00560?

📙 Short Answer Type Questions (2–3 marks)

Define fundamental and derived quantities with two examples each.
Why is it important to have standard units of measurement?
What are systematic errors and how can they be minimized?
Convert 5 km/h into m/s using dimensional analysis.
Define dimensional formula. What is the dimensional formula of force?

📗 Numerical Questions (Calculation Based)

Convert 36 km/h into m/s.
A boy runs 100 meters in 10 seconds. What is his speed in m/s and km/h?
The mass of a block is 2 kg and its volume is 0.001 m³. Find its density and give the dimensional formula of density.
A force of 10 N is applied on a body of mass 2 kg. Find the acceleration.
If the length of a rod is 3.50 m, how many significant figures are there?

📕 Long Answer Type Questions (4–5 marks)

Explain SI system of units. Write the seven SI base units.
What is dimensional analysis? Write two uses of it with examples.
Derive the dimensional formula for work and power.
What is meant by significant figures? State the rules for counting significant figures.
Explain the difference between accuracy and precision with examples.

🧠 Reasoning Based Questions

Why is SI system considered better than other systems like CGS or FPS?
Why do we use scientific notation in physics?
If two quantities have the same dimensions, can they still be physically different? Give example.
Can a quantity have dimensions but no unit? Explain with example.

Here are 20 important MCQs (Multiple Choice Questions) based on Chapter: Units and Measurement (Class 9 CBSE Physics).

📘 Units and Measurement – MCQs (Class 9 Physics)

✅ 1 to 10 – Concept Based Questions

The SI unit of length is:
A. Kilometre
B. Centimetre
C. Meter
D. Inch
The SI unit of mass is:
A. Gram
B. Milligram
C. Kilogram
D. Pound
What is the dimensional formula of velocity?
A. [M⁰ L¹ T⁰]
B. [M⁰ L¹ T⁻¹]
C. [M¹ L⁰ T⁻²]
D. [M⁰ L⁻¹ T⁻¹]
Which of the following is a derived quantity?
A. Mass
B. Length
C. Force
D. Time
1 kilometre = ?
A. 10 m
B. 100 m
C. 1000 m
D. 0.1 m
What is the SI unit of work?
A. Newton
B. Joule
C. Watt
D. Calorie
Which instrument is best for measuring the diameter of a wire?
A. Meter scale
B. Measuring tape
C. Vernier caliper
D. Screw gauge
Significant figures in 0.0450 are:
A. 2
B. 3
C. 4
D. 1
The number 3.0500 has how many significant figures?
A. 3
B. 4
C. 5
D. 2
Which of the following is a fundamental quantity?
A. Area
B. Volume
C. Density
D. Temperature

✅ 11 to 20 – Application Based Questions

What is the dimensional formula of force?
A. [M¹ L¹ T⁻²]
B. [M¹ L² T⁻³]
C. [M⁰ L¹ T⁻¹]
D. [M¹ L⁰ T²]
Which of the following quantities has dimension of [M¹ L² T⁻²]?
A. Power
B. Work
C. Pressure
D. Velocity
A student runs 60 meters in 6 seconds. His speed is:
A. 10 m/s
B. 20 m/s
C. 6 m/s
D. 5 m/s
1 light year is approximately:
A. 9.46 × 10¹⁵ m
B. 3.00 × 10⁸ m
C. 6.02 × 10²³ m
D. 1.60 × 10⁻¹⁹ m
Which is not an SI base unit?
A. Mole
B. Newton
C. Second
D. Kelvin
Vernier caliper is used to measure:
A. Time
B. Small length
C. Mass
D. Area
The unit of power is:
A. Joule
B. Newton
C. Watt
D. Pascal
The dimensional formula of pressure is:
A. [M¹ L⁻¹ T⁻²]
B. [M¹ L² T⁻²]
C. [M⁰ L⁻² T⁻¹]
D. [M⁻¹ L³ T⁻²]
Which of the following has no dimension?
A. Force
B. Angle
C. Work
D. Density
The dimensional formula of acceleration is:
A. [M⁰ L¹ T⁻¹]
B. [M⁰ L¹ T⁻²]
C. [M¹ L⁻¹ T⁻²]
D. [M¹ L¹ T⁻²]