Prerequisites
Before diving into SI units, make sure you understand:
- Basic arithmetic and scientific notation
- The concept of physical quantities (length, mass, time, etc.)
Why Do We Need Standard Units?
The SI System (Système International)
The International System of Units (SI) is the modern form of the metric system, adopted globally for scientific measurements.
Key Features:
- Universal acceptance across the world
- Based on fundamental physical constants (since 2019)
- Decimal system (easy conversions using powers of 10)
Seven SI Base Units
These are the fundamental units from which all other units are derived:
| Physical Quantity | SI Base Unit | Symbol | Definition (2019) |
|---|---|---|---|
| Length | meter | m | Distance light travels in vacuum in 1/299,792,458 second |
| Mass | kilogram | kg | Defined using Planck’s constant (h) |
| Time | second | s | Duration of 9,192,631,770 periods of Cs-133 radiation |
| Electric Current | ampere | A | Flow of 1/(1.602176634×10⁻¹⁹) elementary charges per second |
| Temperature | kelvin | K | 1/273.16 of thermodynamic temperature of water’s triple point |
| Amount of Substance | mole | mol | Exactly 6.02214076×10²³ entities (Avogadro’s number) |
| Luminous Intensity | candela | cd | Luminous intensity in given direction of specific frequency |
Mass, Meter, Mole, Ampere, Temperature, Time, Luminous intensity
Or remember: “Mad Monkeys Make Awesome Tricks Throughout Life”
Why Kilogram is the Only Base Unit with a Prefix
Students often wonder why kilogram (kg) is the base unit, not gram. Historical reasons! The kilogram was originally defined as the mass of 1 liter of water. The prefix “kilo-” stuck even when it became the base unit.
Important: When forming derived units, treat “kilogram” as the base, NOT gram.
SI Derived Units
Derived units are combinations of base units. Here are the most important ones for JEE:
Mechanical Quantities
| Quantity | Unit | Symbol | In Base Units | Formula |
|---|---|---|---|---|
| Area | square meter | m² | m² | — |
| Volume | cubic meter | m³ | m³ | — |
| Velocity | meter per second | m/s | m s⁻¹ | distance/time |
| Acceleration | meter per second² | m/s² | m s⁻² | velocity/time |
| Force | newton | N | kg m s⁻² | mass × acceleration |
| Pressure | pascal | Pa | kg m⁻¹ s⁻² | force/area |
| Work/Energy | joule | J | kg m² s⁻² | force × distance |
| Power | watt | W | kg m² s⁻³ | work/time |
| Momentum | kg m/s | — | kg m s⁻¹ | mass × velocity |
Thermal and Electrical Quantities
| Quantity | Unit | Symbol | In Base Units |
|---|---|---|---|
| Charge | coulomb | C | A s |
| Voltage | volt | V | kg m² s⁻³ A⁻¹ |
| Resistance | ohm | Ω | kg m² s⁻³ A⁻² |
| Capacitance | farad | F | kg⁻¹ m⁻² s⁴ A² |
| Magnetic Field | tesla | T | kg s⁻² A⁻¹ |
| Magnetic Flux | weber | Wb | kg m² s⁻² A⁻¹ |
| Frequency | hertz | Hz | s⁻¹ |
Most Important Derived Unit Formulas:
$$\boxed{\text{Force (N)} = \text{kg} \cdot \text{m/s}^2}$$ $$\boxed{\text{Energy (J)} = \text{N} \cdot \text{m} = \text{kg} \cdot \text{m}^2/\text{s}^2}$$ $$\boxed{\text{Power (W)} = \text{J/s} = \text{kg} \cdot \text{m}^2/\text{s}^3}$$Interactive Demo: Visualize Unit Conversions
Explore how different SI units relate to each other through dimensional analysis.
SI Prefixes
Prefixes help express very large or very small quantities:
Common Prefixes (Must Know for JEE)
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| tera | T | 10¹² | 1 THz = 10¹² Hz |
| giga | G | 10⁹ | 1 GW = 10⁹ W |
| mega | M | 10⁶ | 1 MHz = 10⁶ Hz |
| kilo | k | 10³ | 1 km = 1000 m |
| hecto | h | 10² | 1 hm = 100 m |
| deca | da | 10¹ | 1 dam = 10 m |
| BASE | — | 10⁰ | 1 m |
| deci | d | 10⁻¹ | 1 dm = 0.1 m |
| centi | c | 10⁻² | 1 cm = 0.01 m |
| milli | m | 10⁻³ | 1 mm = 0.001 m |
| micro | μ | 10⁻⁶ | 1 μm = 10⁻⁶ m |
| nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| pico | p | 10⁻¹² | 1 pm = 10⁻¹² m |
| femto | f | 10⁻¹⁵ | 1 fm = 10⁻¹⁵ m |
Large to Small: “The Great Man Krishna Has Done Brave deeds courageously making many noble principles famous”
Tera > Giga > Mega > Kilo > Hecto > Deca > Base > deci > centi > milli > μ micro > nano > pico > femto
Important Non-SI Units (Commonly Used)
| Quantity | Non-SI Unit | SI Equivalent |
|---|---|---|
| Length | 1 angstrom (Å) | 10⁻¹⁰ m |
| Length | 1 light year | 9.46 × 10¹⁵ m |
| Length | 1 parsec | 3.08 × 10¹⁶ m |
| Mass | 1 atomic mass unit (u) | 1.66 × 10⁻²⁷ kg |
| Time | 1 year | 3.156 × 10⁷ s |
| Energy | 1 electron volt (eV) | 1.6 × 10⁻¹⁹ J |
| Energy | 1 calorie | 4.186 J |
| Pressure | 1 atmosphere (atm) | 1.013 × 10⁵ Pa |
| Pressure | 1 bar | 10⁵ Pa |
| Power | 1 horsepower (hp) | 746 W |
Unit Conversion Strategy
Step-by-Step Method:
- Write the given quantity with its unit
- Identify the target unit
- Use conversion factors (multiply by 1 in different forms)
- Cancel units that appear in numerator and denominator
- Calculate the final result
Memory Trick: To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.
Common Mistakes to Avoid
Wrong: $(5 \text{ m})^2 = 5 \text{ m}^2$
Correct: $(5 \text{ m})^2 = 25 \text{ m}^2$
When you square a quantity, you must square BOTH the number and the unit!
Wrong: $v = 20 \text{ km} / 30 \text{ s} = 0.67 \text{ km/s}$
Correct: First convert to same unit system: $v = 20000 \text{ m} / 30 \text{ s} = 666.67 \text{ m/s}$
Wrong: $1 \text{ cm}^3 = 10^{-2} \text{ m}^3$
Correct: $1 \text{ cm}^3 = (10^{-2} \text{ m})^3 = 10^{-6} \text{ m}^3$
The power applies to the prefix too!
Practice Problems
Level 1: JEE Main Basics
Convert 1 kWh (kilowatt-hour) to joules.
Solution: $1 \text{ kWh} = 1000 \text{ W} \times 3600 \text{ s}$ $= 1000 \text{ J/s} \times 3600 \text{ s}$ $= \boxed{3.6 \times 10^6 \text{ J}}$
This is the energy consumed by a 1000 W appliance running for 1 hour!
Express the gravitational constant $G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$ in base SI units.
Solution: $N = \text{kg} \cdot \text{m/s}^2$
$G = 6.67 \times 10^{-11} \frac{(\text{kg} \cdot \text{m/s}^2) \cdot \text{m}^2}{\text{kg}^2}$
$= \boxed{6.67 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2}}$
Level 2: JEE Main/Advanced
A car travels at 90 km/h for 2 hours, then at 60 km/h for 1.5 hours. Find the average speed in m/s.
Solution: Total distance = $90 \times 2 + 60 \times 1.5 = 180 + 90 = 270 \text{ km}$
Total time = $2 + 1.5 = 3.5 \text{ h}$
Average speed = $\frac{270}{3.5} = 77.14 \text{ km/h}$
In m/s: $77.14 \times \frac{5}{18} = \boxed{21.43 \text{ m/s}}$
Level 3: JEE Advanced
If force F, velocity v, and time T are taken as fundamental units, find the dimensions of mass in terms of F, v, and T.
Solution: From $F = ma$, we have $m = \frac{F}{a} = \frac{F}{v/T} = \frac{FT}{v}$
Therefore, $\boxed{[m] = [F][T][v]^{-1}}$
In the new system: $\boxed{m = FTv^{-1}}$
Quick Reference Table
| Conversion | Factor | Example |
|---|---|---|
| km/h → m/s | × 5/18 | 90 km/h = 25 m/s |
| m/s → km/h | × 18/5 | 10 m/s = 36 km/h |
| liters → m³ | × 10⁻³ | 1 L = 0.001 m³ |
| cm³ → m³ | × 10⁻⁶ | 1 cm³ = 10⁻⁶ m³ |
| eV → J | × 1.6×10⁻¹⁹ | 1 eV = 1.6×10⁻¹⁹ J |
| year → s | × 3.156×10⁷ | 1 year ≈ π×10⁷ s |
Related Topics
Within Units and Measurements
- Dimensions — Dimensional formulas of physical quantities
- Dimensional Analysis — Checking equations and deriving formulas
- Errors — Understanding measurement precision
- Significant Figures — Precision in calculations
Connected Chapters
- Kinematics — Applying units to motion problems
- Newton’s Laws — Force units and applications
- Work-Energy-Power — Energy unit conversions
- Electrostatics — Electrical unit systems
Math Connections
- Powers and Exponents — Scientific notation
- Ratio and Proportion — Unit conversions