Chapter 1: Units and Measurements || CLASS 12 NOTES

Chapter 1: Units and Measurements

1. Need for Measurement

Measurement is essential to compare physical quantities and express them in numerical form.

• Provides accuracy in science and engineering
• Helps in standardization
• Ensures consistency in experiments

2. Units of Measurement

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

Systems of Units:

• CGS (Centimeter-Gram-Second)
• MKS (Meter-Kilogram-Second)
• FPS (Foot-Pound-Second)
• SI System (International System of Units)

3. SI Units

Fundamental Units

Quantity	Unit	Symbol
Length	Meter	m
Mass	Kilogram	kg
Time	Second	s
Electric Current	Ampere	A
Temperature	Kelvin	K
Amount of Substance	Mole	mol
Luminous Intensity	Candela	cd

Derived Units

• Velocity = m/s
• Force = Newton (kg·m/s²)
• Work = Joule
• Pressure = Pascal

4. Significant Figures

Significant figures are meaningful digits in a measurement.

Rules:

• All non-zero digits are significant
• Zeros between digits are significant
• Leading zeros are not significant
• Trailing zeros in decimal are significant

Operations Rules

• Add/Subtract → least decimal places
• Multiply/Divide → least significant figures

5. Uncertainty in Measurement

Every measurement has some error.

• Absolute Error: Difference between measured and true value
• Relative Error: Ratio of absolute error to true value
• Percentage Error: Relative error × 100

Formula:
Percentage Error = (Absolute Error / True Value) × 100

6. Dimensions of Physical Quantities

Dimensions represent physical quantities in terms of base quantities.

• Length → [L]
• Mass → [M]
• Time → [T]

Examples

• Velocity = [L T⁻¹]
• Force = [M L T⁻²]
• Energy = [M L² T⁻²]

7. Dimensional Analysis

It is used to check correctness of equations and derive relations.

Applications

• Checking dimensional consistency
• Converting units
• Deriving formulas

Example:
Force = Mass × Acceleration
[M L T⁻²] = [M] × [L T⁻²]

8. MCQ One-Liners

• SI unit of force is Newton.
• SI unit of pressure is Pascal.
• Number of fundamental units in SI system is 7.
• Dimensional formula of velocity is [L T⁻¹].
• Dimensional formula of force is [M L T⁻²].
• Significant figures in 0.0045 = 2.
• Significant figures in 2.300 = 4.
• Unit of work is Joule.
• Unit of power is Watt.
• Least count determines accuracy of instrument.
• Derived units are obtained from fundamental units.
• Dimensional formula of energy is [M L² T⁻²].
• SI unit of temperature is Kelvin.
• Absolute error is always positive.
• Percentage error = (Absolute Error / True Value) × 100.
• CGS system uses cm, g, s.
• MKS system uses m, kg, s.
• Trailing zeros are significant only if decimal is present.
• Dimensional analysis cannot determine numerical constants.
• Unit of density is kg/m³.

9. Numerical Problems with Solutions

1. Calculate Percentage Error

Measured value = 98, True value = 100

Solution:
Absolute Error = |100 - 98| = 2
Percentage Error = (2 / 100) × 100 = 2%

2. Significant Figures

Find significant figures in 0.00560

Solution:
Leading zeros are not significant
Digits 5, 6, 0 are significant
Answer = 3 significant figures

3. Dimensional Formula

Find dimensional formula of Force

Solution:
Force = Mass × Acceleration
= M × (L T⁻²)
= [M L T⁻²]

4. Unit Conversion

Convert 1 km into meters

Solution:
1 km = 1000 m
Answer = 1000 m

5. Density Calculation

Mass = 10 kg, Volume = 2 m³

Solution:
Density = Mass / Volume
= 10 / 2 = 5 kg/m³

6. Addition with Significant Figures

12.5 + 3.42 = ?

Solution:
Answer = 15.92 → round to least decimal places (1 decimal)
Final Answer = 15.9

7. Multiplication with Significant Figures

2.5 × 3.42 = ?

Solution:
Answer = 8.55 → least significant figures = 2
Final Answer = 8.6

8. Relative Error

Absolute error = 0.2, Measured value = 10

Solution:
Relative Error = 0.2 / 10 = 0.02

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