Study Notes
Unit in Physics
Core Idea
A unit is a fixed and accepted standard used to measure any physical quantity.
- If we say length = 5 meters → meter is the unit.
- If speed = 20 m/s → m/s is the unit.
Without a unit, a number has no physical meaning.
10 — meaningless
10 m — meaningful
In IOE MCQ, sometimes they test conceptual clarity like:
- "Which of the following is a unit?"
- "Which is not a unit but a quantity?"
Be sharp: Quantity = numerical value × unit
System of Units
Different systems define different standard units for fundamental quantities like mass, length, and time.
Classical Systems
| Quantity | CGS System | FPS System | MKS System |
|---|---|---|---|
| Length | centimeter (cm) | foot (ft) | meter (m) |
| Mass | gram (g) | pound (lb) | kilogram (kg) |
| Time | second (s) | second (s) | second (s) |
Understanding the Logic
- CGS → Centimeter, Gram, Second
- FPS → Foot, Pound, Second
- MKS → Meter, Kilogram, Second
IOE Trap:
- Don’t confuse gram (CGS) with kilogram (MKS).
- FPS is rarely used in scientific calculations now.
SI System (International System of Units)
SI system is an extension of MKS system.
It includes all fundamental quantities, not just length, mass, and time.
Seven Fundamental SI Units
| Quantity | SI Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Luminous intensity | candela | Cd |
| Amount of substance | mole | mol |
Exam Note
- There are 7 fundamental units.
- Don’t include radian or steradian in this list (common MCQ trap).
- SI unit of temperature is Kelvin, not degree Celsius.
Types of Units
There are three categories:
1. Fundamental Units
- Independent of other units.
- Total = 7
- Examples: m, kg, s, A, K, mol, Cd
They form the base of dimensional analysis.
2. Supplementary Units
These are purely geometrical.
| Quantity | Unit | Symbol |
|---|---|---|
| Plane angle | radian | rad |
| Solid angle | steradian | sr |
MCQ Trap:
- Many students wrongly count them among fundamental units.
- They are supplementary (historically treated separately).
3. Derived Units
These are formed from fundamental units.
Examples:
- Velocity → \( m/s \)
- Acceleration → \( m/s^2 \)
- Force → \( kg \cdot m/s^2 \)
- Pressure → \( N/m^2 \)
Key Concept:
Derived unit = combination of fundamental units raised to powers.
In dimensional analysis, everything reduces to:
\[
M^a L^b T^c I^d \Theta^e N^f J^g
\]
SI Prefixes (Powers of Ten)
Used to express very large or very small quantities.
Large Multiples
| Power | Prefix | Symbol |
|---|---|---|
| \(10^{24}\) | Yotta | Y |
| \(10^{21}\) | Zetta | Z |
| \(10^{18}\) | Exa | E |
| \(10^{15}\) | Peta | P |
| \(10^{12}\) | Tera | T |
| \(10^{9}\) | Giga | G |
| \(10^{6}\) | Mega | M |
| \(10^{3}\) | kilo | k |
| \(10^{2}\) | hecto | h |
| \(10^{1}\) | deca | da |
Small Multiples
| Power | Prefix | Symbol |
|---|---|---|
| \(10^{-1}\) | deci | d |
| \(10^{-2}\) | centi | c |
| \(10^{-3}\) | milli | m |
| \(10^{-6}\) | micro | \( \mu \) |
| \(10^{-9}\) | nano | n |
| \(10^{-12}\) | pico | p |
| \(10^{-15}\) | femto | f |
| \(10^{-18}\) | atto | a |
| \(10^{-21}\) | zepto | z |
| \(10^{-24}\) | yocto | y |
Order of Magnitude (Very Important for IOE)
- Size of nucleus ≈ \(10^{-14}\) m
- Size of atom ≈ \(10^{-10}\) m
IOE Trick:
They may ask:
- "Which is larger?"
- "How many times bigger is atom than nucleus?"
\[ \frac{10^{-10}}{10^{-14}} = 10^4 \]
Atom is \(10^4\) times larger than nucleus.
Common Mistakes in MCQs
- Writing symbol of kilo as K (wrong) → Correct: k
- Writing Kelvin as °K (wrong) → Correct: K
- Confusing gram and kilogram in dimensional equations
- Forgetting that electric current is fundamental
Quick Elimination Strategy
If an option includes:
- Degree Celsius as fundamental unit → eliminate.
- radian as fundamental unit → eliminate.
- gram as SI base unit → eliminate.
Practice MCQs
1. Which of the following is NOT a fundamental SI unit?
A. Kelvin
B. Mole
C. Radian
D. Ampere
Answer
C. Radian
2. The size of an atom is of order:
A. \(10^{-14}\) m
B. \(10^{-10}\) m
C. \(10^{-6}\) m
D. \(10^{-3}\) m
Answer
B. \(10^{-10}\) m
3. Which system uses kilogram as unit of mass?
A. CGS
B. FPS
C. MKS
D. Both C and SI
Answer
D. Both C and SI
Summary
- Unit = standard reference for measurement.
- CGS, FPS, MKS are classical systems.
- SI system has 7 fundamental units.
- Radian and steradian are supplementary.
- Derived units come from combinations of base units.
- Prefixes help express powers of ten.
- Atom ≈ \(10^{-10}\) m, nucleus ≈ \(10^{-14}\) m.
- Always think in terms of MCQ elimination.
Master this topic because dimensional analysis and unit conversion questions are guaranteed scoring areas in IOE.