Physical Quantities and Units

Physical quantities are measured in units. The seven SI base (fundamental) quantities are: length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd). Memory aid: 'Mary Kept Saving All The Money Carefully' (Metre, Kg, Second, Ampere, Kelvin/Temp, Mole, Candela). Derived units are combinations of base units, e.g., force = kg m s^-2 (newton), energy = kg m^2 s^-2 (joule). Supplementary units: radian (plane angle) and steradian (solid angle), now treated as dimensionless derived units. A complete set of base + derived units forms a 'system of units' (CGS, MKS, SI).

SI prefixes scale units: tera (10^12), giga (10^9), mega (10^6), kilo (10^3), milli (10^-3), micro (10^-6), nano (10^-9), pico (10^-12), femto (10^-15). Useful astronomical/atomic units: 1 light year = 9.46 x 10^15 m; 1 parsec = 3.08 x 10^16 m = 3.26 light years; 1 astronomical unit (AU) = 1.496 x 10^11 m; 1 angstrom = 10^-10 m; 1 fermi = 10^-15 m. Mass: 1 atomic mass unit (u) = 1.66 x 10^-27 kg; 1 quintal = 100 kg; 1 metric tonne = 1000 kg. Tip: parsec > light year > AU. Remember 1 parsec is the distance at which 1 AU subtends 1 arcsecond.

Parallax measures large distances. If a distant object is viewed from two points separated by basis b, and the parallax angle is theta (in radians), distance D = b / theta. Example: The Moon is observed from two points on Earth 6400 km apart, with parallax angle 1.5 degrees. Convert: theta = 1.5 x (pi/180) = 0.0262 rad. D = b/theta = 6.4 x 10^6 / 0.0262 = 2.44 x 10^8 m. Remember theta MUST be in radians (arc = radius x angle). For angular diameter alpha of a planet of diameter d at distance D: d = alpha x D, with alpha in radians.

Every numerical answer in NEET Physics is a number × a unit, so a shaky grip on units silently costs marks in every mechanics, thermo and electricity question. Units & Measurement itself contributes about 1 direct question (4 marks) most years, and the unit-conversion habit you build here protects the other 44 questions.

Why it matters

A physical quantity is anything you can measure. It needs a magnitude and a unit. Quantities are either fundamental (base) — chosen independently — or derived, built by multiplying/dividing base quantities.

The 7 SI base quantities

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).

Handy prefixes and non-SI lengths

Prefixes: giga 10⁹, mega 10⁶, kilo 10³, milli 10⁻³, micro 10⁻⁶ (μ), nano 10⁻⁹, pico 10⁻¹², femto 10⁻¹⁵.

• 1 ångström (Å) = 10⁻¹⁰ m; 1 fermi = 10⁻¹⁵ m
• 1 astronomical unit (AU) = 1.496 × 10¹¹ m
• 1 light year = 9.46 × 10¹⁵ m; 1 parsec = 3.08 × 10¹⁶ m ≈ 3.26 ly

Exam Tricks & Tips

• 🎯 Remember candela and mole are base units — students wrongly call them derived.
• 🎯 1 parsec > 1 light year (≈ 3.26 ly). Ordering AU < ly < parsec is a common MCQ.
• 🎯 Angle (rad) and solid angle (sr) are dimensionless but still carry units.
• 🎯 Derived units named after scientists are lowercase words (newton, joule, watt) but capital symbols (N, J, W).
• 🎯 1 AU is the mean Earth–Sun distance; a parsec is defined via a 1 arc-second parallax over 1 AU.
• ❌ Do not confuse energy and torque: both are N·m, but only energy is called joule — never call torque joule.

Expected exam pattern

Matching base units, converting light-year/parsec/AU, or picking the correctly written SI symbol. Occasionally a parallax or angular-size calculation.

Quick recap

7 base units (m, kg, s, A, K, mol, cd) + 2 supplementary (rad, sr). Memorise prefix powers and astronomical lengths (AU < ly < parsec). Always carry the unit through every calculation.

Cover the answer, recall, then check. 11 cards on SI units and measurement basics.

Q1. Name the 7 SI base quantities and their units.
A1. Length (m), Mass (kg), Time (s), Electric current (A), Temperature (K), Amount of substance (mol), Luminous intensity (cd).

Q2. What are the two SI supplementary units?
A2. Radian (rad) for plane angle, steradian (sr) for solid angle. Both are dimensionless.

Q3. 1 light year = ? metres.
A3. 9.46 × 10¹⁵ m (distance light travels in one year).

Q4. 1 parsec equals how many metres and how many light years?
A4. 3.08 × 10¹⁶ m ≈ 3.26 light years.

Q5. 1 astronomical unit (AU) = ?
A5. 1.496 × 10¹¹ m — the mean Earth–Sun distance.

Q6. Order AU, light year and parsec by increasing size.
A6. AU < light year < parsec.

Q7. 1 ångström and 1 fermi in metres?
A7. 1 Å = 10⁻¹⁰ m; 1 fermi = 10⁻¹⁵ m.

Q8. Prefixes: nano, pico, micro — which powers of 10?
A8. nano = 10⁻⁹, pico = 10⁻¹², micro = 10⁻⁶.

Q9. Which base unit measures amount of substance, and how many entities does it contain?
A9. The mole (mol); 1 mole contains Avogadro number 6.022 × 10²³ entities.

Q10. Is angle a fundamental quantity?
A10. No. Plane angle is a supplementary, dimensionless quantity measured in radian.

Q11. How is 1 parsec defined?
A11. The distance at which 1 AU subtends an angle of 1 arc-second (1/3600 degree).

Key formulas

• Physical quantity = numerical value × unit; n₁u₁ = n₂u₂ (smaller unit ⇒ larger number).
• SI base units: m, kg, s, A, K, mol, cd.
• Dimensional formulae: velocity [LT⁻¹], force [MLT⁻²], energy [ML²T⁻²], power [ML²T⁻³], pressure [ML⁻¹T⁻²].
• Homogeneity principle: every term of a physical equation has identical dimensions.
• Unit conversion: n₂ = n₁(M₁/M₂)^a(L₁/L₂)^b(T₁/T₂)^c.
• Derived units combine base units (e.g. newton = kg·m·s⁻²).

Usage: use dimensional homogeneity to check any formula and to convert between unit systems.