The SI System of Units

Units and Measurements opens Class 11 Physics and is a guaranteed 3–4 mark scorer in boards (usually one 1-mark unit question plus a dimensional/error problem). Every numerical answer you write all year must carry the correct SI unit — miss it and you lose marks even when the physics is right.

Why it matters

A physical quantity is measured against a standard called a unit. The SI (Système International) system, adopted in 1971, is the internationally agreed decimal system built on seven base units from which every other unit is derived.

The seven SI base units

Base 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

Two supplementary units complete the set: the radian (rad) for plane angle and the steradian (sr) for solid angle. Derived units are combinations, e.g. force in newton (N = kg·m·s⁻²), energy in joule (J = kg·m²·s⁻²).

Key ideas

• A good unit is well-defined, invariable, easily reproducible and of convenient size.
• Prefixes scale units in powers of ten: nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), kilo (10³), mega (10⁶), giga (10⁹).
• The metre is now defined via the speed of light: the distance light travels in 1/299,792,458 s.

Exam Tricks & Tips

• 🎯 Mnemonic for base quantities: "My Lovely Teacher Calls The Moon Luminous" → Mass, Length, Time, Current, Temperature, Mole, Luminous intensity.
• 🎯 Kelvin takes no degree sign (write 5 K, not 5°K); symbols are never pluralised (10 kg, not 10 kgs).
• 🎯 Unit symbols named after people are capitalised (N, J, Pa, W) but the full name is lowercase (newton, joule).
• 🎯 Always leave a space between number and unit (5 m, not 5m).
• 🎯 Learn newton, joule, watt, pascal in base units — a direct 1-mark board question.
• ❌ Common mistake: calling candela/mole derived units — they are base units; luminous intensity and amount of substance are fundamental.

Expected exam pattern

1-mark: "Name the SI base unit of …". 2-mark: express a derived unit (e.g. watt) in base units. MCQ: match quantity to unit or identify a non-base quantity.

Quick recap

Seven base units (m, kg, s, A, K, mol, cd) + two supplementary (rad, sr). Everything else is derived. Memorise the base quantities, the prefix ladder, and how newton/joule/watt break into base units.

Cover the answer, recall, then check. 12 cards on SI units.

Q1. How many base units are there in the SI system?
A1. Seven — metre, kilogram, second, ampere, kelvin, mole, candela.

Q2. What is the SI base unit of amount of substance?
A2. The mole (mol).

Q3. Name the two supplementary SI units.
A3. Radian (rad) for plane angle and steradian (sr) for solid angle.

Q4. What is the SI base unit of luminous intensity?
A4. The candela (cd).

Q5. Express the newton in SI base units.
A5. 1 N = 1 kg·m·s⁻².

Q6. Express the joule in SI base units.
A6. 1 J = 1 kg·m²·s⁻².

Q7. Express the watt in SI base units.
A7. 1 W = 1 kg·m²·s⁻³.

Q8. What does the prefix "micro" (µ) stand for?
A8. 10⁻⁶.

Q9. In which year was the SI system internationally adopted?
A9. 1971.

Q10. What are the requirements of a good standard unit?
A10. Well-defined, invariable (unchanging), easily reproducible, and of convenient size.

Q11. How is the metre currently defined?
A11. The distance travelled by light in vacuum in 1/299,792,458 of a second.

Q12. What is the SI unit of temperature and its symbol?
A12. The kelvin, symbol K (no degree sign).

Every measurement you ever report is really a comparison against an agreed yardstick — the unit. The SI system is the world's shared set of yardsticks so a "metre" in Delhi means the same as a "metre" in Paris.

Definition / core idea

A physical quantity is anything that can be measured (length, time, current). Its measure = (numerical value) × (unit). The SI system (Système International d'Unités) defines 7 base units from which all others are built.

Deep explanation

Beginner — the 7 base quantities

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

Memory hook: "Mrs LKA MTC" is clumsy — better: "Kind Men And Some Master Chefs Cook" for Kelvin, Metre, Ampere, Second, Mole, Candela… choose any peg that sticks for you; the exam just wants the 7.

Intermediate — derived units

All other units are derived by combining base units through the defining equation.

• Speed = length/time → m/s
• Force = mass × acceleration → kg·m/s² = newton (N)
• Energy = force × distance → kg·m²/s² = joule (J)
• Pressure = force/area → N/m² = pascal (Pa)

Advanced — coherence and standards

SI is a coherent system: derived units follow from base units with no extra numerical factors (1 N = 1 kg·m/s² exactly). Since 2019 all base units are fixed by defining constants of nature (e.g. the second uses the caesium-133 hyperfine frequency 9,192,631,770 Hz; the metre uses the speed of light c = 299,792,458 m/s). This makes standards reproducible in any lab. There are also two supplementary units: radian (rad) for plane angle and steradian (sr) for solid angle.

Worked example

Express a car's speed of 72 km/h in SI base units.
72 km/h = 72 × (1000 m) / (3600 s) = 72000/3600 = 20 m/s.
So the SI value is 20 m/s. Note the shortcut: km/h → m/s means multiply by 5/18 (72 × 5/18 = 20).

Real-world application

GPS, satellite navigation and international trade all depend on one agreed SI standard so that engineers, pilots and doctors worldwide read the same numbers without conversion errors.

Exam tricks & shortcuts

• km/h → m/s: × 5/18; m/s → km/h: × 18/5. Memorise this pair; it appears in almost every kinematics MCQ.
• The candela and mole are the two base units students forget — expect a "which is NOT a base unit?" question (watch for newton, coulomb, watt as traps — those are derived).

Key formulas

• Seven base units: length metre (m), mass kilogram (kg), time second (s), electric current ampere (A), temperature kelvin (K), amount mole (mol), luminous intensity candela (cd).
• Derived unit = combination of base units. e.g. force newton N = kg·m·s⁻², energy joule J = kg·m²·s⁻², power watt W = J·s⁻¹, pressure pascal Pa = N·m⁻².
• Unit conversion: value × (ratio of units). e.g. 1 km/h = 1000 m / 3600 s = 5/18 m/s.
• Prefixes: kilo 10³, centi 10⁻², milli 10⁻³, micro 10⁻⁶, nano 10⁻⁹, mega 10⁶, giga 10⁹.
• Angle (plane): θ = arc/radius = l/r → radian (rad); solid angle Ω = area/r² → steradian (sr).

Units must be consistent on both sides of any physical equation.

Worked Example

Problem: The density of mercury is 13.6 g cm⁻³. Express this value in the SI unit of density (kg m⁻³), showing the unit conversion explicitly.

Solution:
Density in the SI system must be expressed in kilograms per cubic metre (kg m⁻³), since the SI base units for mass and length are the kilogram and the metre.

Step 1 — Convert the mass unit: 1 g = 10⁻³ kg.

Step 2 — Convert the volume unit: 1 cm = 10⁻² m, so 1 cm³ = (10⁻²)³ m³ = 10⁻⁶ m³.

Step 3 — Substitute both conversions:
13.6 g cm⁻³ = 13.6 × (10⁻³ kg) / (10⁻⁶ m³)
= 13.6 × 10⁻³⁺⁶ kg m⁻³
= 13.6 × 10³ kg m⁻³.

Step 4 — Write the final value:
13.6 × 10³ kg m⁻³ = 13600 kg m⁻³.

Answer: 13.6 g cm⁻³ = 1.36 × 10⁴ kg m⁻³ (13600 kg m⁻³).