📑 Topics on this page (Jump to Topic):
📌 1. Fundamental Quantities & SI Units
The SI system (Système International, 1960) has 7 fundamental quantities; all others are derived quantities built from them.
| Fundamental quantity | SI 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 |
- Supplementary units: plane angle — radian (rad), solid angle — steradian (sr).
- Since 2019 all 7 base units are defined by constants of nature (e.g. Planck constant h); the kilogram is no longer based on a metal cylinder.
- CGS = centimetre-gram-second; MKS = metre-kilogram-second; FPS = foot-pound-second.
📌 2. Derived Units & Units Named after Scientists
| Quantity | SI unit | In base units |
|---|---|---|
| Force | newton (N) | kg·m/s² |
| Work/Energy | joule (J) | N·m |
| Power | watt (W) | J/s |
| Pressure | pascal (Pa) | N/m² |
| Frequency | hertz (Hz) | 1/s |
| Charge | coulomb (C) | A·s |
| Potential difference | volt (V) | J/C |
| Resistance | ohm (Ω) | V/A |
| Capacitance | farad (F) | C/V |
| Magnetic flux | weber (Wb) | V·s |
| Magnetic field | tesla (T) | Wb/m² |
| Inductance | henry (H) | Wb/A |
| Radioactivity | becquerel (Bq) | 1/s |
| Power of lens | dioptre (D) | 1/m |
💡 Memory Tip: "Newton-Joule-Watt-Pascal" — force, energy, power, pressure — remember in this order.
📌 3. Practical Units & Conversions
| Unit | Value | Measures |
|---|---|---|
| Light year | ≈ 9.46 × 10¹⁵ m | Distance (not time!) |
| Astronomical unit (AU) | ≈ 1.496 × 10¹¹ m | Mean Earth–Sun distance |
| Parsec | ≈ 3.26 ly | Astronomical distance (largest) |
| Angstrom (Å) | 10⁻¹⁰ m | Wavelength |
| Fermi | 10⁻¹⁵ m | Nuclear size |
| Nautical mile | 1852 m | Sea distance |
| Horsepower (hp) | ≈ 746 W | Power |
| kWh (unit) | 3.6 × 10⁶ J | Electrical energy |
| Calorie | ≈ 4.186 J | Heat |
| Electron volt | 1.6 × 10⁻¹⁹ J | Energy |
| Bar | 10⁵ Pa | Pressure |
- Temperature: K = °C + 273.15; °F = (9/5)°C + 32. Celsius and Fahrenheit are equal at −40°.
- Normal body temperature ≈ 37 °C = 98.6 °F = 310 K.
- 1 km/h = 5/18 m/s; 1 m/s = 3.6 km/h.
📌 4. Scalars, Vectors, Dimensions & Instruments
- Scalars (magnitude only): mass, speed, distance, time, energy, work, temperature, pressure, electric current.
- Vectors (magnitude + direction): displacement, velocity, acceleration, force, momentum, weight, impulse, torque.
- Dimensions: force [MLT⁻²], energy [ML²T⁻²], power [ML²T⁻³], pressure [ML⁻¹T⁻²]. Work and torque have the same dimensions.
- Vernier callipers (least count 0.1 mm) and screw gauge (0.01 mm) measure small lengths.
⚠️ Exam Traps:
- Light year is a unit of distance, not time.
- Electric current has direction but is a scalar (it does not follow vector addition).
- kWh is a unit of energy, not power.
📌 5. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. Which of the following is an SI base unit? Practice
Correct answer: (A)
Candela is the base unit of luminous intensity; the rest are derived.
Candela is the base unit of luminous intensity; the rest are derived.
Q2. Light year is a unit of: Practice
Correct answer: (D)
Distance travelled by light in one year ≈ 9.46 × 10¹⁵ m.
Distance travelled by light in one year ≈ 9.46 × 10¹⁵ m.
Q3. What is the SI unit of pressure? Practice
Correct answer: (C)
1 Pa = 1 N/m²; bar and torr are practical units.
1 Pa = 1 N/m²; bar and torr are practical units.
Q4. At what temperature do Celsius and Fahrenheit scales read the same? Practice
Correct answer: (B)
Putting C = F in °F = 9C/5 + 32 gives C = −40.
Putting C = F in °F = 9C/5 + 32 gives C = −40.
Q5. Which of the following is a vector quantity? Practice
Correct answer: (D)
Momentum = mass × velocity; velocity is a vector, so momentum is too.
Momentum = mass × velocity; velocity is a vector, so momentum is too.
Q6. 1 horsepower (hp) is approximately equal to: Practice
Correct answer: (A)
1 hp ≈ 746 W (550 ft·lbf/s).
1 hp ≈ 746 W (550 ft·lbf/s).
Q7. One "unit" in an electricity bill equals: Practice
Correct answer: (C)
1 unit = 1 kWh = 3.6 × 10⁶ J of energy.
1 unit = 1 kWh = 3.6 × 10⁶ J of energy.
Q8. The SI unit of power of a lens is: Practice
Correct answer: (A)
P = 1/f (in metres); unit dioptre (m⁻¹).
P = 1/f (in metres); unit dioptre (m⁻¹).
Q9. Which pair has the same dimensions? Practice
Correct answer: (A)
Both are [ML²T⁻²] — but work is scalar while torque is a vector.
Both are [ML²T⁻²] — but work is scalar while torque is a vector.
Q10. The SI unit of magnetic flux is: Practice
Correct answer: (B)
Weber is for flux; tesla (Wb/m²) is for magnetic field.
Weber is for flux; tesla (Wb/m²) is for magnetic field.
Q11. Normal human body temperature in kelvin is about: Practice
Correct answer: (B)
37 + 273 = 310 K.
37 + 273 = 310 K.
Q12. One nautical mile equals: Practice
Correct answer: (C)
Nautical mile = 1852 m; statute mile = 1609 m.
Nautical mile = 1852 m; statute mile = 1609 m.
Q13. The mean distance between the Earth and the Sun is called: Practice
Correct answer: (D)
1 AU ≈ 1.496 × 10⁸ km.
1 AU ≈ 1.496 × 10⁸ km.
Q14. A speed of 72 km/h equals: Practice
Correct answer: (B)
72 × 5/18 = 20 m/s.
72 × 5/18 = 20 m/s.
Q15. What is the dimensional formula of force? Practice
Correct answer: (C)
F = ma = kg·m/s² → [MLT⁻²].
F = ma = kg·m/s² → [MLT⁻²].
Q16. The usual least count of a screw gauge is: Practice
Correct answer: (D)
Screw gauge measures to 0.01 mm; vernier callipers to 0.1 mm.
Screw gauge measures to 0.01 mm; vernier callipers to 0.1 mm.
Q17. Which of the following is NOT a unit of energy? Practice
Correct answer: (A)
Watt is a unit of power (J/s).
Watt is a unit of power (J/s).
Q18. Choose the correct statement about electric current. Practice
Correct answer: (B)
Current is a base quantity (ampere) and does not obey vector addition, so it is a scalar.
Current is a base quantity (ampere) and does not obey vector addition, so it is a scalar.
Q19. Which is the largest unit of distance? Practice
Correct answer: (C)
1 parsec ≈ 3.26 light years.
1 parsec ≈ 3.26 light years.
Q20. Which unit is NOT named after a scientist? Practice
Correct answer: (D)
Candela comes from Latin for "candle"; the others honour Hertz, Kelvin and Ampère.
Candela comes from Latin for "candle"; the others honour Hertz, Kelvin and Ampère.