CLASS 11 PHYSICS • UNITS AND MEASUREMENTS

Physical Quantities and SI Units

Premium notes on physical quantities, SI units, base and derived units, prefixes, scientific notation, order of magnitude, unit conversion, numericals and PYQs.

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1. Physical Quantities

A physical quantity is any measurable property of a body or phenomenon. A complete measurement has a numerical value and a unit, such as 5 m, 2 kg or 10 s.

Characteristics

It must be measurable.
It has magnitude.
It is expressed with a unit.
It may be scalar or vector.

Scalar Quantities

Scalars have magnitude only. Examples: mass, time, temperature, distance, speed and energy.

Vector Quantities

Vectors have magnitude and direction. Examples: displacement, velocity, acceleration, force and momentum.

Examples Table

Example	Measurement	Type
Length of table	2 m	Scalar
Velocity of car	20 m s^-1 east	Vector
Mass of book	0.5 kg	Scalar
Force on box	10 N right	Vector

2. Fundamental Quantities

Fundamental quantities are independent physical quantities that cannot be expressed in terms of other quantities. SI has seven base quantities.

Quantity	SI Unit	Symbol	Brief Explanation
Length	metre	m	Distance between two points; used in displacement, height and wavelength.
Mass	kilogram	kg	Amount of matter; base unit includes prefix kilo by historical convention.
Time	second	s	Duration of events; essential in motion and oscillations.
Electric Current	ampere	A	Rate of flow of electric charge.
Temperature	kelvin	K	Thermodynamic temperature scale.
Amount of Substance	mole	mol	Amount containing Avogadro number of entities.
Luminous Intensity	candela	cd	Intensity of visible light in a given direction.

3. Derived Quantities

Derived quantities are formed by combining fundamental quantities through multiplication, division or powers.

Derived Quantity	Formation	SI Unit
Area	length × breadth	m²
Volume	length × breadth × height	m³
Velocity	displacement / time	m s^-1
Acceleration	change in velocity / time	m s^-2
Momentum	mass × velocity	kg m s^-1
Force	mass × acceleration	kg m s^-2 or N
Work / Energy	force × displacement	kg m² s^-2 or J
Power	work / time	kg m² s^-3 or W
Pressure	force / area	kg m^-1 s^-2 or Pa
Density	mass / volume	kg m^-3

4. SI System

History

The SI system developed from the metric system and is maintained internationally for uniform scientific communication.

Advantages

It is decimal, coherent, internationally accepted and easy for conversion using prefixes.

Need

Standardization prevents confusion in experiments, trade, engineering and scientific research.

5. Base Units

The seven SI base units form the foundation of all derived units.

Quantity	Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric Current	ampere	A
Temperature	kelvin	K
Amount of Substance	mole	mol
Luminous Intensity	candela	cd

Exam Tip: Symbols are case-sensitive. kg, m, s, A, K, mol and cd must be written correctly.

6. Supplementary Units

Radian and steradian were historically called supplementary units. In the modern SI, they are treated as dimensionless derived units.

Radian

Radian measures plane angle. θ = arc length / radius.

Steradian

Steradian measures solid angle in three-dimensional space.

7. SI Prefixes

SI prefixes express very large and very small quantities compactly.

Prefix	Symbol	Power of 10
yotta	Y	10²⁴
zetta	Z	10²¹
exa	E	10¹⁸
peta	P	10¹⁵
tera	T	10¹²
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
hecto	h	10²
deca	da	10¹
deci	d	10^-1
centi	c	10^-2
milli	m	10^-3
micro	μ	10^-6
nano	n	10^-9
pico	p	10^-12
femto	f	10^-15
atto	a	10^-18
zepto	z	10^-21
yocto	y	10^-24

Memory idea: learn powers in steps of 3: kilo 10³, mega 10⁶, giga 10⁹; milli 10^-3, micro 10^-6, nano 10^-9.

8. Scientific Notation

Scientific notation writes a number as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Large Number

300000000 m s^-1 = 3.00 × 10⁸ m s^-1

Small Number

0.000001 m = 1 × 10^-6 m

Rule

Move decimal to make one non-zero digit before decimal, then count moves as power of 10.

Use

It simplifies calculations involving atomic and astronomical quantities.

9. Order of Magnitude

Order of magnitude is the nearest power of 10 that estimates a quantity.

Quantity	Approximate Value	Order of Magnitude
Radius of Earth	6.4 × 10⁶ m	10⁷ m
Speed of Light	3.00 × 10⁸ m s^-1	10⁸ m s^-1
Mass of Electron	9.1 × 10^-31 kg	10^-30 kg
Size of Atom	1 × 10^-10 m	10^-10 m

10. Unit Conversion

Unit conversion uses conversion factors without changing the physical quantity.

Conversion	Equivalent	Method
1 km	1000 m	multiply by 10³
1 cm	10^-2 m	multiply by 10^-2
1 hour	3600 s	multiply by 3600
1 g	10^-3 kg	multiply by 10^-3
1 eV	1.6 × 10^-19 J	multiply by 1.6 × 10^-19

11. Important Tables

Physical Constants

Constant	Symbol	Value
Speed of light	c	3.00 × 10⁸ m s^-1
Planck constant	h	6.63 × 10^-34 J s
Electronic charge	e	1.6 × 10^-19 C
Avogadro constant	N_A	6.022 × 10²³ mol^-1

Quick Unit Conversion

Conversion	Factor
km to m	× 10³
m to cm	× 10²
kg to g	× 10³
minute to second	× 60

12. Solved Numericals

CBSE Numerical

Question: Convert 2.5 km into metre.

Given: 2.5 km

Formula: 1 km = 1000 m

Substitution: 2.5 × 1000

Calculation: 2500 m

Final Answer: 2.5 km = 2500 m

Exam Tip: Always replace prefix first.

NEET Numerical

Question: Write 0.00045 m in scientific notation.

Given: 0.00045 m

Formula: a × 10ⁿ

Substitution: 4.5 × 10^-4 m

Calculation: Decimal moved 4 places

Final Answer: 4.5 × 10^-4 m

Exam Tip: Coefficient must be between 1 and 10.

JEE Main Numerical

Question: Convert 72 km h^-1 into m s^-1.

Given: 72 km h^-1

Formula: multiply by 5/18

Substitution: 72 × 5/18

Calculation: 20

Final Answer: 20 m s^-1

Exam Tip: Use 5/18 for km h^-1 to m s^-1.

JEE Advanced Numerical

Question: Find SI unit of pressure using force/area.

Given: Pressure = force/area

Formula: N / m²

Substitution: kg m s^-2 / m²

Calculation: kg m^-1 s^-2

Final Answer: kg m^-1 s^-2 or Pa

Exam Tip: Derive from base units.

IB Numerical

Question: Convert 3.2 μs to seconds.

Given: 3.2 μs

Formula: 1 μs = 10^-6 s

Substitution: 3.2 × 10^-6 s

Calculation: 3.2 × 10^-6

Final Answer: 3.2 × 10^-6 s

Exam Tip: Micro means 10^-6.

IGCSE Numerical

Question: Convert 500 g to kg.

Given: 500 g

Formula: 1 g = 10^-3 kg

Substitution: 500 × 10^-3

Calculation: 0.5 kg

Final Answer: 0.5 kg

Exam Tip: Divide gram by 1000.

A-Level Numerical

Question: Convert 2 eV to joule.

Given: 2 eV

Formula: 1 eV = 1.6 × 10^-19 J

Substitution: 2 × 1.6 × 10^-19

Calculation: 3.2 × 10^-19 J

Final Answer: 3.2 × 10^-19 J

Exam Tip: eV is an energy unit.

13. PYQ and Exam-Style Questions

CBSE Exam-style Question

Question: Distinguish between fundamental and derived quantities.

Solution: Length is fundamental, velocity is derived from length/time.

Final Answer: Fundamental quantities are independent; derived quantities are formed from them.

Exam Tip: Give examples.

NEET Exam-style Question

Question: Which is not an SI base unit: metre, kelvin, newton, second?

Solution: Newton is derived unit of force.

Final Answer: newton

Exam Tip: Know base units.

JEE Main Exam-style Question

Question: The SI unit of energy in base units is?

Solution: Energy = work = force × displacement.

Final Answer: kg m² s^-2

Exam Tip: Start from force.

JEE Advanced Conceptual Question

Question: Why is unit consistency necessary in equations?

Solution: This is principle of homogeneity.

Final Answer: Only quantities with same dimensions can be added or equated.

Exam Tip: Use dimensional check.

IB Physics Exam-style Question

Question: Why are SI units preferred in scientific communication?

Solution: They prevent ambiguity.

Final Answer: They are internationally accepted and coherent.

Exam Tip: Mention standardization.

IGCSE Exam-style Question

Question: What does milli mean?

Solution: Example: 1 mm = 10^-3 m.

Final Answer: 10^-3

Exam Tip: Common prefix.

A-Level Exam-style Question

Question: Explain order of magnitude.

Solution: Used for quick comparison and estimation.

Final Answer: Nearest power of 10 estimate of a quantity.

Exam Tip: Estimate before calculating.