🏠 NEET Home

NEET 2027 · Physics · Class 11 · Ch. 1 Units and Measurement

SI Units & Derived Units

Seven base units, twenty-two special names and a table of practical units. Together with dimensional formulae, unit identification is the largest single slice of this chapter's questions.

PRIORITY 1TOPIC 2 + 10 OF 1520 QUESTIONS3 PYQ-BASEDNCERT §1.2, Tables 1.1–1.2

01Concept in plain language

A measurement is a comparison. Saying a rod is 3 metres long means it is three times as long as an agreed reference. The reference is the unit; the three is the numerical value. Neither means anything alone.

Physics has hundreds of quantities but does not need hundreds of independent units, because the quantities are related to one another. Choose a small set of units for a few quantities and every other unit follows. The chosen ones are the base units; the ones that follow are derived units. Together they form a system of units.

Why SI won

Three systems were in wide use before SI. CGS took centimetre, gram and second; FPS (British) took foot, pound and second; MKS took metre, kilogram and second. SI — Système International d'Unités — extends MKS to seven base units and is decimal throughout, so every conversion is a shift of the decimal point rather than an awkward factor like 12 or 5280.

What changed in 2019

Until May 2019 the kilogram was a physical object: a platinum–iridium cylinder kept near Paris. Objects can be scratched, contaminated or lost. The revision presented in NCERT Table 1.1 replaced every artefact with a fixed constant of nature. Each of the seven base units is now defined by declaring one constant to have an exact numerical value, and letting the unit fall out of that declaration. The metre, for instance, is whatever length makes the speed of light come out to exactly 299 792 458 m s⁻¹.

What NCERT explicitly says you need not memorise

The footnote to Table 1.1 states that the numerical values of the defining constants need not be remembered or asked in a test. What is asked is the pairing — which constant defines which unit — and the names and symbols of the seven base units. Learn those pairings; skip the digits.

02The seven, and what fixes them

THE SEVEN SI BASE UNITS — EVERYTHING ELSE IS DERIVED FROM THESESI7 base unitsmlengthkgmassstimeAcurrentKtemperaturemolamountcdluminous int.Radian (rad) and steradian (sr) ride alongside as dimensionless units for plane and solid angle.
Fig. 1 — The seven base units. Radian and steradian sit outside the ring because they are dimensionless.
2019 REDEFINITION · SEVEN FIXED CONSTANTS DEFINE SEVEN UNITSΔνCs9 192 631 770 Hzsecondc299 792 458 m s−¹metreh6.626 070 15 × 10−³⁴ J skilograme1.602 176 634 × 10−¹⁹ Camperek1.380 649 × 10−²³ J K−¹kelvinNA6.022 140 76 × 10²³ mol−¹moleKcd683 lm W−¹candelaThe kilogram prototype cylinder was retired in May 2019 — no SI unit now rests on an artefact.
Fig. 2 — The 2019 redefinition. Read this as seven pairs; the pairing is examinable, the digits are not.
PREFIX LADDER · EACH RUNG IS A FACTOR OF 1000 (EXCEPT CENTI)T10¹²teraG10⁹gigaM10⁶megak10³kiloc10−²centim10−³milliμ10−⁶micron10−⁹nanop10−¹²picof10−¹⁵femtoArea picks up the prefix squared, volume cubed: 1 cm² = 10−⁴ m², 1 cm³ = 10−⁶ m³. That single line fixes most conversion mistakes.
Fig. 3 — Prefixes step in thousands, with centi and deci as the everyday exceptions. The squaring and cubing rule beneath the ladder prevents most conversion errors.

03The seven base units

learn column 3 and column 4 as pairs
Base quantityUnitSymbolFixed by (2019)Dimension
Lengthmetremc = 299 792 458 m s⁻¹L
Masskilogramkgh = 6.626 070 15 × 10⁻³⁴ J sM
TimesecondsΔνCs = 9 192 631 770 HzT
Electric currentampereAe = 1.602 176 634 × 10⁻¹⁹ CA
Thermodynamic temperaturekelvinKk = 1.380 649 × 10⁻²³ J K⁻¹K
Amount of substancemolemolNA = 6.022 140 76 × 10²³ mol⁻¹mol
Luminous intensitycandelacdKcd = 683 lm W⁻¹cd

Two dimensionless companions

Radian (rad) for plane angle, dθ = ds/r, and steradian (sr) for solid angle, dΩ = dA/r². Both are ratios of like quantities, so both are dimensionless — yet both have names and symbols. A full circle is 2π rad; a full sphere is 4π sr.

04Derived units with special names

These are the derived units NEET expects on sight, together with their base-unit expansion. The expansion column is what turns a recall question into a two-line calculation.

QuantityUnitSymbolIn base unitsNamed after
FrequencyhertzHzs⁻¹Heinrich Hertz
ForcenewtonNkg m s⁻²Isaac Newton
Pressure, stresspascalPakg m⁻¹ s⁻² (= N m⁻²)Blaise Pascal
Energy, work, heatjouleJkg m² s⁻² (= N m)James Prescott Joule
PowerwattWkg m² s⁻³ (= J s⁻¹)James Watt
Electric chargecoulombCA sCharles-Augustin de Coulomb
Potential difference, emfvoltVkg m² s⁻³ A⁻¹ (= J C⁻¹)Alessandro Volta
CapacitancefaradFkg⁻¹ m⁻² s⁴ A² (= C V⁻¹)Michael Faraday
ResistanceohmΩkg m² s⁻³ A⁻² (= V A⁻¹)Georg Simon Ohm
ConductancesiemensSkg⁻¹ m⁻² s³ A² (= Ω⁻¹)Werner von Siemens
Magnetic fluxweberWbkg m² s⁻² A⁻¹ (= V s)Wilhelm Weber
Magnetic flux densityteslaTkg s⁻² A⁻¹ (= Wb m⁻²)Nikola Tesla
InductancehenryHkg m² s⁻² A⁻² (= Wb A⁻¹)Joseph Henry
Activity of a radionuclidebecquerelBqs⁻¹Henri Becquerel
Absorbed dosegrayGym² s⁻² (= J kg⁻¹)Louis Harold Gray
Illuminanceluxlxcd sr m⁻²—
Luminous fluxlumenlmcd sr—
Celsius temperaturedegree Celsius°CK (offset by 273.15)Anders Celsius

05Practical units retained outside SI

NCERT Table 1.2 lists units that are not SI but are permitted alongside it because they are convenient. Every one of these has appeared in a conversion question.

UnitSymbolValue in SIWhere it is used
Astronomical unitAU1.496 × 10¹¹ mmean Sun–Earth distance
Light yearly9.46 × 10¹⁵ mdistance light travels in one year
Parsecpc3.08 × 10¹⁶ m= 3.26 ly; parallax of one arcsecond
AngstromÅ10⁻¹⁰ matomic sizes; H atom ≈ 0.5 Å
Fermifm10⁻¹⁵ mnuclear sizes
Barnb10⁻²⁸ m²nuclear cross-section (= 100 fm²)
Unified atomic mass unitu1.66 × 10⁻²⁷ kg1/12 of a carbon-12 atom
Quintalq100 kgretained for trade
Tonnet10³ kgretained for trade
Caratc200 mggemstones
LitreL10⁻³ m³= 1 dm³
Hectareha10⁴ m²= 1 hm²
Area10² m²= 1 dam²
Barbar10⁵ Pa = 0.1 MPaexactly 100 kPa
Standard atmosphereatm1.013 × 10⁵ Pa101 325 Pa exactly
CurieCi3.7 × 10¹⁰ s⁻¹old unit of activity
RoentgenR2.58 × 10⁻⁴ C kg⁻¹old unit of exposure
Degree°π/180 radplane angle
Dayd86 400 s24 h
Yeary3.156 × 10⁷ s365.25 d

06Prefixes and the rules for writing units

multiples above the line, sub-multiples below
PrefixSymbolFactor
teraT10¹²
gigaG10⁹
megaM10⁶
kilok10³
hectoh10²
decada10¹
decid10⁻¹
centic10⁻²
millim10⁻³
microμ10⁻⁶
nanon10⁻⁹
picop10⁻¹²
femtof10⁻¹⁵
attoa10⁻¹⁸

Writing conventions NEET has tested

  • Unit symbols are never pluralised: 10 kg, never 10 kgs.
  • No full stop after a symbol unless it ends a sentence: 5 m, not 5 m.
  • A unit named after a person is written in lower case but its symbol is capitalised: newton and N, kelvin and K, pascal and Pa. The exception is the litre, whose symbol L is capitalised to avoid confusion with the digit 1.
  • Leave a space between the number and the symbol: 5 kg, not 5kg. The exception is the degree symbol for angle: 30°.
  • Only one prefix at a time: use nm, never mμm. And the kilogram is the only base unit that already contains a prefix, so multiples are built on the gram: 10⁶ kg is a megagram (tonne), never a kilo-kilogram.
  • Prefixes attach to the whole unit before any power is taken: cm² means (cm)² = 10⁻⁴ m², not c(m²).

07Exceptions and traps

Same dimension, different name, on purpose

Hertz and becquerel are both s⁻¹. Gray and sievert are both J kg⁻¹. Newton metre (torque) and joule (energy) are both kg m² s⁻². SI keeps the names distinct because the physics differs, not because the dimensions do. A question asking 'which have the same dimensions?' and one asking 'are these the same quantity?' have opposite answers.

Dimensionless quantities can still have units

Radian, steradian and the decibel are all dimensionless. Refractive index and strain are dimensionless and unitless. The two properties are independent, and options are often written to exploit the confusion.

The kilogram is the odd one out

It is the only base unit whose name already carries a prefix. This is why the mass prefix table is built on the gram, and why in dimensional work you must remember that 1 kg = 10³ g when converting to CGS — a factor that trips up nearly every joule-to-erg conversion.

Celsius is not a base unit

Kelvin is the base unit. The degree Celsius is a derived unit of the same size, offset by 273.15. A difference of 1 °C equals a difference of 1 K exactly, which is why specific heat may be quoted in J kg⁻¹ °C⁻¹ with no change in the number. An absolute temperature, however, must be in kelvin.

08Numbers to remember

these carry directly into conversion questions in the next file
ConversionValue
1 light year9.46 × 10¹⁵ m
1 astronomical unit (AU)1.496 × 10¹¹ m
1 parsec3.08 × 10¹⁶ m = 3.26 light years
1 Ångström10⁻¹⁰ m
1 fermi10⁻¹⁵ m
1 barn10⁻²⁸ m²
1 u1.66 × 10⁻²⁷ kg (≡ 931.5 MeV)
1 atm1.013 × 10⁵ Pa = 760 mm Hg
1 bar10⁵ Pa exactly
1 curie3.7 × 10¹⁰ Bq
1 year3.156 × 10⁷ s
1 day86 400 s
1 degreeπ/180 rad ≈ 0.01745 rad
1 radian≈ 57.3°
1 eV1.6 × 10⁻¹⁹ J
1 calorie4.2 J
1 kWh3.6 × 10⁶ J
1 poise0.1 Pa s
1 J10⁷ erg
1 N10⁵ dyne

09Scientists behind the units

high-frequency names in matching and statement questions
NameUnitWhat it measures
Isaac Newtonnewton (N)force
James Prescott Joulejoule (J)energy, work, heat
James Wattwatt (W)power
Blaise Pascalpascal (Pa)pressure and stress
Heinrich Hertzhertz (Hz)frequency
Charles-Augustin de Coulombcoulomb (C)electric charge
Alessandro Voltavolt (V)potential difference
Georg Simon Ohmohm (Ω)resistance
Michael Faradayfarad (F)capacitance
Werner von Siemenssiemens (S)conductance
Nikola Teslatesla (T)magnetic flux density
Wilhelm Weberweber (Wb)magnetic flux
Joseph Henryhenry (H)inductance
Henri Becquerelbecquerel (Bq)radioactive activity
Anders Celsiusdegree Celsius (°C)temperature (derived, not base)
William Thomson, Lord Kelvinkelvin (K)thermodynamic temperature (base)
André-Marie Ampèreampere (A)electric current (base)
Jean Poiseuillepoise (P)dynamic viscosity (CGS)
George Gabriel Stokesstokes (St)kinematic viscosity (CGS)

10Twenty worked questions

About the PYQ labels

Items tagged PYQ follow the wording and structure of questions that have appeared in NEET/AIPMT papers. Year labels are indicative and worth cross-checking against the official NTA paper. Every numerical value on this page was recomputed before printing.

Q01Base vs derived

Which of the following pairs consists only of SI base units?

  1. kelvin and mole
  2. newton and kelvin
  3. joule and mole
  4. ampere and coulomb
Show full solution
Given
Four pairs of units.
Asked
The pair in which both members are base units.
Concept
There are exactly seven base units: m, kg, s, A, K, mol, cd. Anything else — however familiar — is derived.
Formula
base set = {m, kg, s, A, K, mol, cd}
Baby steps
  1. Kelvin is the base unit of thermodynamic temperature. ✓
  2. Mole is the base unit of amount of substance. ✓
  3. Newton, joule and coulomb are all derived (N = kg m s⁻², J = N m, C = A s).
  4. So only the first pair qualifies.
Answer
(a) kelvin and mole
Why not others
(a)Correct — both are in the list of seven.
(b)Newton is derived from kg, m and s.
(c)Joule is derived; only mole is base.
(d)Ampere is base but coulomb is derived (C = A s).
Shortcut
Memory line: My Kind Sister Always Keeps Mints Close — metre, kilogram, second, ampere, kelvin, mole, candela.
Where it goes wrong
Coulomb feels fundamental because charge feels fundamental. SI chose current, not charge, as the base electrical quantity — so the ampere is base and the coulomb is derived.
Q02PYQ · NEET 2024Derived unit

The SI unit of specific heat capacity is:

  1. J kg⁻¹
  2. J mol⁻¹ K⁻¹
  3. J K⁻¹
  4. J kg⁻¹ K⁻¹
Show full solution
Given
Q = m s ΔΘ.
Asked
SI unit of s.
Concept
Read the defining equation as a sentence: heat per unit mass per unit rise in temperature.
Formula
s = Q / (m ΔΘ)
Baby steps
  1. Q is in joules.
  2. Divide by mass in kilograms → J kg⁻¹.
  3. Divide by temperature rise in kelvin → J kg⁻¹ K⁻¹.
  4. Note that a rise of 1 K equals a rise of 1 °C, so J kg⁻¹ °C⁻¹ is numerically identical.
Answer
(d) J kg⁻¹ K⁻¹
Why not others
(a)That is latent heat — no temperature change is involved in a phase change.
(b)That is molar specific heat capacity.
(c)That is heat capacity of the whole body, not per kilogram.
(d)Correct.
Shortcut
Three cousins, three units: heat capacity J K⁻¹, specific heat J kg⁻¹ K⁻¹, molar specific heat J mol⁻¹ K⁻¹. The middle word tells you the denominator.
Where it goes wrong
Latent heat and specific heat are routinely swapped. Latent heat has no K in it at all.
Q03Base-unit expansion

A derived unit equals kg m² s⁻³ A⁻¹. That unit is the:

  1. watt
  2. ohm
  3. volt
  4. weber
Show full solution
Given
The base-unit combination kg m² s⁻³ A⁻¹.
Asked
Which named SI unit this is.
Concept
Break the combination into a familiar unit divided by another. kg m² s⁻³ is the watt, so the whole thing is watt per ampere.
Formula
V = W / A = J C⁻¹
Baby steps
  1. kg m² s⁻³ = watt.
  2. Dividing by A gives W A⁻¹.
  3. Power = VI, so V = P/I = W A⁻¹. ✓
  4. Hence the unit is the volt.
Answer
(c) volt
Why not others
(a)Watt is kg m² s⁻³ with no A at all.
(b)Ohm is kg m² s⁻³ A⁻² — two powers of A.
(c)Correct.
(d)Weber is kg m² s⁻² A⁻¹ — note s⁻², not s⁻³.
Shortcut
Volt and weber differ by exactly one second, because Wb = V s. Ohm and volt differ by exactly one ampere, because Ω = V A⁻¹.
Where it goes wrong
Confusing volt (s⁻³) with weber (s⁻²). Count the seconds before deciding.
Q04Base-unit expansion

One tesla, expressed in SI base units, is:

  1. kg m s⁻² A⁻¹
  2. kg s⁻² A⁻¹
  3. kg m² s⁻² A⁻¹
  4. kg m⁻¹ s⁻² A⁻¹
Show full solution
Given
F = BIl, or equivalently T = Wb m⁻².
Asked
The tesla written out in base units.
Concept
Use B = F/(Il) and substitute the base units of force, current and length.
Formula
B = F / (I l)
Baby steps
  1. [F] → kg m s⁻².
  2. Divide by A and by m: (kg m s⁻²)/(A · m).
  3. The metre cancels completely.
  4. T = kg s⁻² A⁻¹.
Answer
(b) kg s⁻² A⁻¹
Why not others
(a)A stray metre remains — that would be N A⁻¹, not N A⁻¹ m⁻¹.
(b)Correct. Cross-check: Wb m⁻² = (kg m² s⁻² A⁻¹)/m² = kg s⁻² A⁻¹. ✓
(c)That is the weber, not the tesla.
(d)Over-cancelled by one power of length.
Shortcut
Tesla is the only common magnetic unit with no metre in it. If your answer has an m in it, you have found the weber instead.
Where it goes wrong
Both routes (F/Il and Wb/m²) must agree. If they do not, you have mis-copied an exponent — run both as a self-check.
Q05Odd one out

Which of the following is not a unit of energy?

  1. newton second
  2. erg
  3. calorie
  4. kilowatt hour
Show full solution
Given
Four units.
Asked
The one that does not measure energy.
Concept
Expand each unit into base units and compare with the joule, kg m² s⁻².
Formula
J = kg m² s⁻² = N m
Baby steps
  1. N s = (kg m s⁻²)(s) = kg m s⁻¹ — that is momentum / impulse. ✗
  2. erg = 10⁻⁷ J (CGS energy unit). ✓
  3. calorie = 4.2 J. ✓
  4. kW h = 10³ W × 3600 s = 3.6 × 10⁶ J. ✓
Answer
(a) newton second
Why not others
(a)Correct — newton second is impulse, i.e. momentum.
(b)erg is the CGS unit of energy.
(c)calorie is a heat-energy unit, about 4.2 J.
(d)kilowatt hour is the commercial energy unit, 3.6 × 10⁶ J.
Shortcut
Newton metre is energy; newton second is impulse. One word apart, completely different quantity.
Where it goes wrong
Also worth knowing: electron volt, 1 eV = 1.6 × 10⁻¹⁹ J, is an energy unit despite the word 'volt' in its name.
Q06Practical units

One light year is approximately:

  1. 3.26 × 10¹⁶ m
  2. 1.496 × 10¹¹ m
  3. 9.46 × 10¹² m
  4. 9.46 × 10¹⁵ m
Show full solution
Given
Speed of light c = 3 × 10⁸ m s⁻¹; one year = 3.156 × 10⁷ s.
Asked
One light year expressed in metres.
Concept
A light year is a distance, not a time: the distance light covers in one year.
Formula
1 ly = c × (1 year)
Baby steps
  1. 1 y = 365.25 × 86 400 s = 3.156 × 10⁷ s.
  2. 1 ly = (3 × 10⁸)(3.156 × 10⁷) m.
  3. = 9.47 × 10¹⁵ m.
  4. Standard rounded value: 9.46 × 10¹⁵ m.
Answer
(d) 9.46 × 10¹⁵ m
Why not others
(a)That is the parsec, which is 3.26 light years.
(b)That is the astronomical unit.
(c)Off by 10³ — a common slip when the year is taken as 3.156 × 10⁴ s.
(d)Correct.
Shortcut
Chain them: 1 pc = 3.26 ly, and 1 ly ≈ 63 000 AU. Learn the three in order of size — AU < ly < pc.
Where it goes wrong
NCERT Exercise 1.2(b) asks the reverse: 1 m = ? ly, which is 1.057 × 10⁻¹⁶ ly.
Q07Practical units

One parsec is equal to:

  1. 9.46 × 10¹⁵ m
  2. 1.496 × 10¹¹ m
  3. 3.08 × 10¹⁶ m
  4. 3.26 × 10¹⁵ m
Show full solution
Given
A parsec is the distance at which one astronomical unit subtends one second of arc.
Asked
The parsec in metres.
Concept
Small-angle relation: distance = arc / angle, with the angle converted from arcseconds to radians.
Formula
1 pc = (1 AU) / (1″ in radians)
Baby steps
  1. 1″ = (1/3600)° = (1/3600)(π/180) rad = 4.85 × 10⁻⁶ rad.
  2. 1 pc = 1.496 × 10¹¹ / 4.85 × 10⁻⁶ m.
  3. = 3.08 × 10¹⁶ m.
  4. Equivalently 3.26 light years.
Answer
(c) 3.08 × 10¹⁶ m
Why not others
(a)That is one light year.
(b)That is one astronomical unit.
(c)Correct.
(d)This mixes the two: 3.26 is the number of light years in a parsec, not metres.
Shortcut
Distance ladder in one line: 1 AU = 1.5 × 10¹¹ m → 1 ly = 9.46 × 10¹⁵ m → 1 pc = 3.08 × 10¹⁶ m. Each step is roughly a factor of 60 000, then 3.26.
Where it goes wrong
Option (d) is the classic distractor: right digits, wrong unit. Always check whether the answer is asked in metres or in light years.
Q08Angles

The steradian is the unit of:

  1. plane angle
  2. solid angle
  3. angular velocity
  4. luminous flux
Show full solution
Given
dΩ = dA / r², from NCERT Fig. 1.1(b).
Asked
What the steradian measures.
Concept
Plane angle is arc over radius; solid angle is intercepted area over radius squared. Both are ratios of like quantities, so both are dimensionless.
Formula
dθ = ds/r (radian) · dΩ = dA/r² (steradian)
Baby steps
  1. Plane angle uses a length ratio → radian.
  2. Solid angle uses an area-to-radius-squared ratio → steradian.
  3. Both give M⁰ L⁰ T⁰.
  4. A full sphere subtends 4π sr; a full circle subtends 2π rad.
Answer
(b) solid angle
Why not others
(a)Plane angle uses the radian.
(b)Correct.
(c)Angular velocity uses rad s⁻¹, dimensionally just T⁻¹.
(d)Luminous flux uses the lumen (= cd sr).
Shortcut
Numbers worth carrying: 2π rad in a circle, 4π sr in a sphere, 1 rad ≈ 57.3°, 1° = π/180 rad.
Where it goes wrong
Radian and steradian used to be called 'supplementary units'. In the modern SI they are simply dimensionless derived units. If a question offers 'supplementary unit' as an option, it is using older wording — the physics is unchanged.
Q092019 redefinition

In the SI revision that took effect in 2019, the kilogram was redefined by fixing the numerical value of:

  1. Planck's constant h
  2. Avogadro's number NA
  3. the speed of light c
  4. the elementary charge e
Show full solution
Given
The 2018 CGPM decision, implemented 20 May 2019.
Asked
Which defining constant fixes the kilogram.
Concept
Each of the seven base units is now tied to one exactly-fixed constant of nature. The mapping is worth learning as seven pairs.
Formula
h = 6.626 070 15 × 10⁻³⁴ J s (exact)
Baby steps
  1. h has the unit J s = kg m² s⁻¹.
  2. The metre is already fixed by c and the second by ΔνCs.
  3. So fixing h leaves only the kilogram undetermined — and therefore defines it.
  4. The platinum–iridium prototype kilogram was retired at the same time.
Answer
(a) Planck's constant h
Why not others
(a)Correct. NCERT Table 1.1 states this definition directly.
(b)NA fixes the mole.
(c)c fixes the metre.
(d)e fixes the ampere.
Shortcut
The seven pairings: c→metre, ΔνCs→second, h→kilogram, e→ampere, k→kelvin, NA→mole, Kcd→candela.
Where it goes wrong
NCERT footnotes that the numerical values themselves need not be memorised. Learn which constant goes with which unit — that is what gets asked.
Q102019 redefinition

The ampere is now defined by fixing the value of:

  1. the Boltzmann constant k
  2. the caesium frequency ΔνCs
  3. Avogadro's number NA
  4. the elementary charge e
Show full solution
Given
SI base unit definitions after 2019.
Asked
The defining constant for the ampere.
Concept
Charge is current × time. Fixing the size of one elementary charge, together with an already-fixed second, pins down the ampere.
Formula
e = 1.602 176 634 × 10⁻¹⁹ C, where C = A s
Baby steps
  1. e is expressed in coulombs.
  2. 1 C = 1 A s.
  3. The second is already defined by ΔνCs.
  4. So fixing e defines the ampere.
Answer
(d) the elementary charge e
Why not others
(a)k defines the kelvin.
(b)ΔνCs defines the second.
(c)NA defines the mole.
(d)Correct. Note the old force-between-wires definition of the ampere was abandoned in 2019.
Shortcut
If the constant's unit contains the unit you are defining, that is the pairing. e is in coulombs = A s, so e defines the ampere.
Where it goes wrong
The pre-2019 ampere was defined by the force between two parallel current-carrying wires. Older textbooks still print that definition; the rationalised NCERT does not.
Q11Practical units

One barn is equal to:

  1. 10⁻²⁴ m²
  2. 10⁻²⁶ m²
  3. 10⁻²⁸ m²
  4. 10⁻³⁰ m²
Show full solution
Given
NCERT Table 1.2: 1 barn = 100 fm².
Asked
The barn in square metres.
Concept
Convert the fermi to metres first, then square. Areas take the prefix to the second power.
Formula
1 fm = 10⁻¹⁵ m → 1 fm² = 10⁻³⁰ m²
Baby steps
  1. 1 fm = 10⁻¹⁵ m.
  2. 1 fm² = (10⁻¹⁵)² = 10⁻³⁰ m².
  3. 1 barn = 100 fm² = 10² × 10⁻³⁰.
  4. = 10⁻²⁸ m².
Answer
(c) 10⁻²⁸ m²
Why not others
(a)Too large by 10⁴.
(b)Too large by 10² — the factor of 100 was applied in the wrong direction.
(c)Correct. The barn measures nuclear cross-section, roughly the geometric area of a nucleus.
(d)The factor of 100 was ignored.
Shortcut
The whole family of area conversions runs on 'square the prefix': 1 cm² = 10⁻⁴ m², 1 mm² = 10⁻⁶ m², 1 fm² = 10⁻³⁰ m².
Where it goes wrong
Squaring 10⁻¹⁵ as 10⁻³⁰ is right; writing it as 10⁻²² (adding instead of doubling) is the standard slip.
Q12Practical units

Standard atmospheric pressure is:

  1. exactly 10⁵ Pa
  2. 1.013 × 10⁵ Pa
  3. 0.1 MPa
  4. 760 Pa
Show full solution
Given
NCERT Table 1.2.
Asked
The value of 1 atm in pascals.
Concept
Distinguish the bar (a round 10⁵ Pa by definition) from the atmosphere (101 325 Pa, set by a 760 mm mercury column).
Formula
1 atm = 101 325 Pa ; 1 bar = 10⁵ Pa
Baby steps
  1. 1 atm supports 760 mm of mercury.
  2. P = hρg = (0.76)(13 600)(9.8) ≈ 1.013 × 10⁵ Pa.
  3. NCERT quotes 101 325 Pa = 1.013 × 10⁵ Pa.
  4. The bar is defined as exactly 10⁵ Pa, which is about 1.3% smaller.
Answer
(b) 1.013 × 10⁵ Pa
Why not others
(a)That is one bar, not one atmosphere.
(b)Correct.
(c)0.1 MPa = 10⁵ Pa, again the bar.
(d)760 is the height in millimetres of mercury, not a pressure in pascals.
Shortcut
1 atm ≈ 1.013 bar. If a question offers both a round 10⁵ and a 1.013 × 10⁵, read carefully which unit is named.
Where it goes wrong
Option (d) confuses a length (760 mm Hg) with a pressure. Torr is the correct unit there: 1 atm = 760 torr.
Q13Base-unit expansion

The SI unit of magnetic flux, and its expression in base units, are:

  1. weber, kg m² s⁻² A⁻¹
  2. tesla, kg s⁻² A⁻¹
  3. henry, kg m² s⁻² A⁻²
  4. volt, kg m² s⁻³ A⁻¹
Show full solution
Given
φ = BA, and Faraday's law e = −dφ/dt.
Asked
Unit of magnetic flux and its base-unit form.
Concept
Two independent routes must agree: field × area, and emf × time.
Formula
Wb = T m² = V s
Baby steps
  1. Route 1: T × m² = (kg s⁻² A⁻¹)(m²) = kg m² s⁻² A⁻¹.
  2. Route 2: V × s = (kg m² s⁻³ A⁻¹)(s) = kg m² s⁻² A⁻¹.
  3. The two agree, so the unit is the weber.
  4. Inductance H = Wb A⁻¹ adds one more A⁻¹.
Answer
(a) weber, kg m² s⁻² A⁻¹
Why not others
(a)Correct.
(b)Tesla is flux density, i.e. flux per unit area.
(c)Henry is inductance, flux per unit current.
(d)Volt is flux per unit time.
Shortcut
One family, three members: Wb (flux), Wb m⁻² = T (flux density), Wb A⁻¹ = H (inductance). Each division tells you what changed.
Where it goes wrong
Mixing weber and tesla is the most common electromagnetism unit error in NEET. Flux is the total; flux density is per unit area.
Q14Named units

The unit 'poise' is used for:

  1. surface tension
  2. pressure
  3. power
  4. coefficient of viscosity
Show full solution
Given
1 poise is the CGS unit named after Jean Poiseuille.
Asked
Which quantity the poise measures.
Concept
Viscosity in SI is Pa s. The CGS equivalent is the poise, and the conversion follows from the dimensional formula M L⁻¹ T⁻¹.
Formula
1 poise = 1 g cm⁻¹ s⁻¹ = 0.1 Pa s
Baby steps
  1. [η] = M L⁻¹ T⁻¹.
  2. CGS: g cm⁻¹ s⁻¹. SI: kg m⁻¹ s⁻¹.
  3. Ratio = (10⁻³ kg)(10⁻² m)⁻¹ = 10⁻³ × 10² = 10⁻¹.
  4. So 1 poise = 0.1 Pa s, i.e. 1 Pa s = 10 poise.
Answer
(d) coefficient of viscosity
Why not others
(a)Surface tension uses N m⁻¹; the CGS unit is dyne cm⁻¹.
(b)Pressure uses pascal or, in CGS, barye.
(c)Power uses watt.
(d)Correct — poise (P), often used as centipoise; water is about 1 cP at room temperature.
Shortcut
Any unit ending in a person's name is derived, never base. Poise→Poiseuille, stokes→Stokes (kinematic viscosity, m² s⁻¹).
Where it goes wrong
Poise measures dynamic viscosity η. Kinematic viscosity ν = η/ρ uses the stokes and has dimensions L² T⁻¹ — a different quantity entirely.
Q15Practical units

One curie is equal to:

  1. 3.7 × 10⁷ s⁻¹
  2. 3.7 × 10⁸ s⁻¹
  3. 3.7 × 10¹⁰ s⁻¹
  4. 3.7 × 10¹² s⁻¹
Show full solution
Given
NCERT Table 1.2.
Asked
The curie expressed in SI.
Concept
Activity is disintegrations per second. The SI unit is the becquerel, 1 Bq = 1 s⁻¹; the curie is the older, much larger unit.
Formula
1 Ci = 3.7 × 10¹⁰ Bq
Baby steps
  1. Activity has dimensions T⁻¹.
  2. 1 Bq = one disintegration per second.
  3. 1 Ci was originally the activity of 1 g of radium-226.
  4. That works out to 3.7 × 10¹⁰ s⁻¹.
Answer
(c) 3.7 × 10¹⁰ s⁻¹
Why not others
(a)Three orders of magnitude too small.
(b)Two orders too small.
(c)Correct.
(d)Two orders too large.
Shortcut
Group the T⁻¹ family: frequency (Hz), activity (Bq), decay constant, angular velocity, Hubble constant. Same dimension, five different names.
Where it goes wrong
Hz and Bq are dimensionally identical (both s⁻¹) but are kept as separate names because one describes a periodic event and the other a random one. NEET has tested this distinction.
Q16Prefixes

The SI prefix denoting 10⁻¹⁵ is:

  1. pico
  2. femto
  3. atto
  4. nano
Show full solution
Given
The standard SI prefix table.
Asked
Which prefix equals 10⁻¹⁵.
Concept
Below unity the prefixes step in thousands: milli, micro, nano, pico, femto, atto.
Formula
m 10⁻³ · μ 10⁻⁶ · n 10⁻⁹ · p 10⁻¹² · f 10⁻¹⁵ · a 10⁻¹⁸
Baby steps
  1. Count in threes downward from milli.
  2. milli −3, micro −6, nano −9, pico −12, femto −15.
  3. So 10⁻¹⁵ is femto.
  4. The fermi, a nuclear length unit, is exactly one femtometre.
Answer
(b) femto
Why not others
(a)pico is 10⁻¹².
(b)Correct.
(c)atto is 10⁻¹⁸.
(d)nano is 10⁻⁹.
Shortcut
Going up: kilo, mega, giga, tera (3, 6, 9, 12). Going down: milli, micro, nano, pico, femto (−3, −6, −9, −12, −15). Centi and deci are the only everyday exceptions to the step of three.
Where it goes wrong
Centi is 10⁻², not 10⁻³. That single irregularity causes most cm→m errors.
Q17Practical units

One unified atomic mass unit (1 u) equals:

  1. 1.66 × 10⁻²⁷ kg
  2. 1.66 × 10⁻²⁴ kg
  3. 9.1 × 10⁻³¹ kg
  4. 1.67 × 10⁻²⁵ kg
Show full solution
Given
1 u is one-twelfth of the mass of a neutral carbon-12 atom.
Asked
1 u expressed in kilograms.
Concept
One mole of carbon-12 weighs 12 g and contains NA atoms, so 1 u = 1 g / NA.
Formula
1 u = 10⁻³ kg / (6.022 × 10²³)
Baby steps
  1. Mass of one C-12 atom = 12 g / 6.022 × 10²³.
  2. Divide by 12: 1 u = 1 g / 6.022 × 10²³.
  3. = 10⁻³ / 6.022 × 10²³ kg.
  4. = 1.66 × 10⁻²⁷ kg.
Answer
(a) 1.66 × 10⁻²⁷ kg
Why not others
(a)Correct.
(b)That is the mass in grams, not kilograms.
(c)That is the mass of an electron.
(d)Off by two orders of magnitude.
Shortcut
Learn the trio together: electron 9.1 × 10⁻³¹ kg, proton 1.67 × 10⁻²⁷ kg, 1 u 1.66 × 10⁻²⁷ kg. Proton and 1 u are close but not identical.
Where it goes wrong
1 u is also worth 931.5 MeV of energy through E = mc². That conversion appears in the Nuclei chapter and is a standard NEET item.
Q18PYQ · NEET 2019Derived unit

The SI unit of electrical conductance is:

  1. ohm
  2. ohm metre
  3. mho metre
  4. siemens
Show full solution
Given
Conductance G = 1/R.
Asked
SI unit of conductance.
Concept
Conductance is the reciprocal of resistance, so its unit is the reciprocal ohm, given the special name siemens.
Formula
G = 1/R ; S = Ω⁻¹ = A V⁻¹
Baby steps
  1. R is measured in ohms.
  2. G = 1/R → Ω⁻¹.
  3. The SI special name for Ω⁻¹ is the siemens (S).
  4. The older name for the same unit is the mho.
Answer
(d) siemens
Why not others
(a)Ohm is resistance, the reciprocal quantity.
(b)Ohm metre is resistivity ρ, a material property.
(c)Mho metre is not a standard unit; conductivity is S m⁻¹.
(d)Correct.
Shortcut
Four related units, easy to separate: R in Ω, ρ in Ω m, G in S, σ in S m⁻¹. The metre appears exactly where the material property does.
Where it goes wrong
Conductance (S) and conductivity (S m⁻¹) are different quantities. The word ending '-ivity' always signals a material property independent of size.
Q19Unit equivalence

The unit N m⁻¹ is equivalent to:

  1. J m⁻¹
  2. J m⁻³
  3. J m⁻²
  4. J m
Show full solution
Given
Surface tension can be defined either as force per unit length or as surface energy per unit area.
Asked
The equivalent form of N m⁻¹.
Concept
Multiply top and bottom by a metre. N m is a joule, so N m⁻¹ = N m / m² = J m⁻².
Formula
N m⁻¹ = (N m)/m² = J m⁻²
Baby steps
  1. Multiply numerator and denominator by m: (N m)/(m × m).
  2. N m = J.
  3. So N m⁻¹ = J m⁻².
  4. Check dimensionally: both give M T⁻². ✓
Answer
(c) J m⁻²
Why not others
(a)J m⁻¹ is force, i.e. the newton itself.
(b)J m⁻³ is energy density, which equals the pascal.
(c)Correct — both expressions describe surface tension.
(d)J m is not a standard combination.
Shortcut
Three energy-per-something units worth knowing cold: J m⁻¹ = N (force), J m⁻² = N m⁻¹ (surface tension), J m⁻³ = Pa (energy density and pressure).
Where it goes wrong
Energy density and pressure share the pascal. NEET has used this equivalence to disguise questions about the energy stored in a capacitor or a magnetic field.
Q20Practical units

One angstrom equals:

  1. 10⁻⁹ m
  2. 10⁻¹⁰ m
  3. 10⁻¹² m
  4. 10⁻¹⁵ m
Show full solution
Given
NCERT Exercise 1.14 defines 1 Å = 10⁻¹⁰ m.
Asked
The angstrom in metres.
Concept
The angstrom is the natural scale for atoms: a hydrogen atom is about 0.5 Å in radius, so about 1 Å across.
Formula
1 Å = 10⁻¹⁰ m = 0.1 nm
Baby steps
  1. 1 nm = 10⁻⁹ m.
  2. 1 Å = 0.1 nm = 10⁻¹⁰ m.
  3. Atomic volume of one H atom ≈ (4/3)π(0.5 × 10⁻¹⁰)³ ≈ 5.2 × 10⁻³¹ m³.
  4. For a mole, multiply by NA: ≈ 3.2 × 10⁻⁷ m³ (NCERT Ex. 1.14).
Answer
(b) 10⁻¹⁰ m
Why not others
(a)That is the nanometre, ten times larger.
(b)Correct.
(c)That is the picometre.
(d)That is the femtometre or fermi, the nuclear scale.
Shortcut
Scale ladder for the exam: nucleus 10⁻¹⁵ m, atom 10⁻¹⁰ m, virus 10⁻⁷ m, human 10⁰ m, Earth 10⁷ m, Sun–Earth 10¹¹ m, galaxy 10²¹ m.
Where it goes wrong
NCERT Exercise 1.15 uses this to show the molar volume of a gas is about 10⁴ times the actual molecular volume — the reason gases are so compressible.