NEET Physics · NCERT Class 11

Units and Measurements notes

Units & SI System, Significant Figures, Errors in Measurement, Dimensions & Dimensional Formulae and Dimensional Analysis & Applications — explained topic by topic with key points, formulas, memory tricks and common mistakes.

  • 6 topics
  • 49 min read
  • 24 formulas
  • 36 PYQs
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1

Chapter Overview

6 min

Physics begins with measurement because every law becomes meaningful only when quantities are measured and compared. A physical quantity has a numerical value and a unit, such as 5 m or 2 kg. This chapter builds the language of physics: fundamental and derived quantities, SI units, significant figures, errors, dimensions and dimensional analysis. In NEET, this chapter is high-scoring because questions are often direct, formula-based and concept-checking. It also supports mechanics, heat, waves, electricity and modern physics. Mastering unit conversion, significant figures, error propagation and dimensional formulae helps avoid silly mistakes and quickly verify options in MCQs.

Key points6

  • NEET frequently asks SI units, dimensional formulae, significant figures and percentage error.
  • Units may change with system, but dimensions of a physical quantity remain the same.
  • Accuracy means closeness to true value; precision means closeness among repeated measurements.
  • In addition and subtraction, result follows least decimal places; in multiplication and division, result follows least significant figures.
  • For powers, fractional powers and products, percentage errors combine according to powers.
  • Dimensionless quantities may have units, such as angle in radian, but their dimensional formula is [M0L0T0].

Memory tricks2

Seven SI Base Quantities: Mnemonic: 'Long Men Take Current Kilo Mole Candles' = Length, Mass, Time, Current, Kelvin temperature, Mole, Candela.

NEET Measurement Flow: Remember: Unit → Significant figures → Error → Dimension → Analysis. This is the usual order of solving measurement questions.

Examples2

Real-Life Measurement

A doctor measuring body temperature, a mechanic measuring screw diameter and a physicist measuring time period all need standard units and uncertainty estimates.

NEET Use

If an option has dimension [ML2T-2], it may represent work, energy or torque, so dimensions help eliminate wrong choices quickly.

Common mistakes3

Confusing Unit and Dimension

Newton and dyne are different units, but both have the same dimension [MLT-2]. Units can change; dimensions do not.

Assuming All Exact Numbers Have Error

Counting numbers and defined constants usually do not limit significant figures; measured quantities do.

Ignoring Powers in Error Propagation

For x = a^2 b, percentage error in x is 2 percentage error in a plus percentage error in b.

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Formulas3

Basic Measurement Form
Physical quantity = numerical value × unit\text{Physical quantity }=\text{ numerical value }×\text{ unit}

Every measured physical quantity is written as a number multiplied by a standard unit.

Physical quantity
Measurable property such as length, mass, time or force
Unit
Standard reference used for comparison
Percentage Error
Percentage error =(Δa/a)×100\text{Percentage error }= (Δa / a) × 100

Gives relative uncertainty in percentage form, useful for NEET numerical questions.

Δa
Absolute error in measured quantity
a
Measured or mean value of the quantity
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2

Units & SI System

8 min

A physical quantity is anything that can be measured, such as length, mass, time, speed or force. It is expressed using a numerical value and a unit. Fundamental quantities are independent base quantities, while derived quantities are obtained from them using mathematical relations. The SI system is the internationally accepted system used in science and NEET. It contains seven base units and many derived units. Older systems such as CGS and FPS are still useful for conversions and historical questions. Prefixes like milli, micro, kilo and mega make very large or very small measurements convenient. NEET questions often test unit symbols, conversions and dimensions together.

Key points6

  • A unit must be well-defined, reproducible, accessible and invariant.
  • SI base unit of mass is kilogram, not gram.
  • Symbols are case-sensitive: m = metre, M = mega, mol = mole.
  • Do not pluralize unit symbols: 5 kg, not 5 kgs.
  • Derived units with special names include newton, joule, watt, pascal, coulomb and volt.
  • Unit conversion can be done by multiplying by conversion factors equal to 1.

Memory tricks2

Base Units: Mnemonic: 'Mr Kg Saw Ampere Kelvin Mole Candela' = metre, kilogram, second, ampere, kelvin, mole, candela.

Small Prefix Order: milli, micro, nano, pico go down by 10^-3 each step: 10^-3, 10^-6, 10^-9, 10^-12.

Examples3

Prefix Conversion

5 km = 5 × 10^3 m = 5000 m. 3 μs = 3 × 10^-6 s.

Derived Unit

Force = mass × acceleration, so SI unit = kg × m s^-2 = kg m s^-2 = newton.

Practice Question

Convert 72 km h^-1 into m s^-1. Answer: 72 × 5/18 = 20 m s^-1.

Common mistakes3

Wrong Capital Letters

Use K for kelvin, not k; use k for kilo, not K. Case matters in SI symbols.

Mixing Units

Do not put mass in grams and length in metres inside one SI formula unless the equation is adjusted.

Calling Radian a Base Unit

Radian was historically called supplementary; modern SI treats it as a dimensionless derived unit.

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Formulas3

Unit Conversion Principle
n1u1=n2u2n1u1 = n2u2

The same physical quantity has different numerical values in different units.

n1, n2
Numerical values in unit systems 1 and 2
u1, u2
Corresponding units
Conversion of Derived Unit
1 unit of Q=MaLbTc1\text{ unit of }Q = M^a L^b T^c

If Q has dimensions [M^aL^bT^c], convert mass, length and time units with their powers.

a,b,c
Powers of mass, length and time in dimensional formula
Q
Derived physical quantity
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3

Significant Figures

7 min

Significant figures are the digits in a measured value that are reliably known, including the first uncertain digit. They indicate the precision of measurement. For example, 2.50 m is more precise than 2.5 m because it has three significant figures. Accuracy means closeness to the true value, while precision means repeatability or closeness of measured values to one another. Significant figure rules are essential in NEET because final numerical answers should not imply more precision than the data allow. The rules differ for addition-subtraction and multiplication-division. Scientific notation makes significant figures clear, especially for numbers containing zeros.

Key points5

  • 0.00450 has 3 significant figures: 4, 5 and final 0.
  • 500 may have 1, 2 or 3 significant figures unless written as 5 × 10^2, 5.0 × 10^2 or 5.00 × 10^2.
  • Exact counted numbers do not limit significant figures.
  • Final rounding should be done at the end, not at every intermediate step.
  • More significant figures generally mean greater precision, not necessarily greater accuracy.

Memory tricks2

Zeros Rule: Remember: 'Left zeros leave, middle zeros matter, decimal-end zeros stay.'

Operations Shortcut: Add/subtract → decimal places. Multiply/divide → significant figures.

Examples3

Worked Addition

12.11 + 18.0 + 1.013 = 31.123. Least decimal places = 1, so answer = 31.1.

Worked Multiplication

4.56 × 1.4 = 6.384. Least significant figures = 2, so answer = 6.4.

Practice MCQ

How many significant figures are in 0.02040? Answer: 4.

Common mistakes3

Counting Leading Zeros

In 0.00052, zeros only locate the decimal point; they are not significant.

Rounding Too Early

Keep extra digits during calculation and round only the final answer.

Using Multiplication Rule for Addition

2.34 + 1.2 must be rounded by decimal places, not total significant figures.

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Formulas3

Scientific Notation
N=a×10nN = a × 10^n
where 1≤a<10\text{where }1 ≤ a < 10

A number is written with clear significant figures using powers of ten.

N
Original number
a
Coefficient containing significant digits
n
Integer power of ten
Addition/Subtraction Rule
Final decimal places = least decimal places among terms\text{Final decimal places }=\text{ least decimal places among terms}

For sums and differences, decimal place precision controls the answer.

Final decimal places
Number of digits retained after decimal in result
terms
Measured values being added or subtracted
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4

Errors in Measurement

9 min

No measurement is perfectly exact because instruments, observers and conditions introduce uncertainty. Error is the difference between measured value and true value, though the true value is usually unknown. Repeated measurements are used to estimate the best value and uncertainty. Errors may be systematic, random or least count errors. Absolute error gives uncertainty in the same unit, relative error compares it with the measured value, and percentage error expresses it as a percent. Error propagation is crucial when measured quantities are combined in formulas. NEET often asks direct calculations of mean absolute error, percentage error and maximum percentage error in derived quantities.

Key points6

  • Systematic errors include instrumental, observational and environmental errors.
  • Random errors can be reduced, not completely removed.
  • Smaller least count generally means more precise instrument.
  • Percentage error has no unit.
  • For x = a^m b^n / c^p, maximum fractional error = m Δa/a + n Δb/b + p Δc/c.
  • In NEET, maximum error is usually asked; signs are ignored and errors are added.

Memory tricks2

Error Types: Mnemonic: 'SIR-L' = Systematic, Instrumental/observational/environmental, Random, Least count.

Propagation Shortcut: Products, quotients and powers: add percentage errors after multiplying by powers.

Examples3

Mean Absolute Error Example

Readings: 2.1, 2.2, 2.3 cm. Mean = 2.2 cm. Absolute errors = 0.1, 0, 0.1 cm. Mean absolute error = 0.067 cm.

Error Propagation Example

If density ρ = m/V, and errors in m and V are 1% and 3%, maximum percentage error in density = 4%.

NEET Shortcut

For T = 2π√(l/g), percentage error in T = 1/2 percentage error in l + 1/2 percentage error in g.

Common mistakes3

Using Signed Errors in Maximum Error

For maximum possible error, take magnitudes and add; do not cancel positive and negative errors.

Confusing Absolute and Relative Error

Absolute error has unit; relative and percentage errors do not have physical units.

Forgetting Power Multiplication

If radius has 2% error, area has 4% error because A ∝ r^2.

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Formulas6

Mean Value
amean =(a1+a2+...+an)/n\text{amean }= (a1 + a2 + ... + an) / n

Best estimate of a measured quantity from repeated observations.

amean
Mean measured value
a1, a2, ..., an
Individual measurements
n
Number of observations
Absolute Error
Δai=∣ai− amean∣Δai = |ai -\text{ amean}|

Magnitude of deviation of an observation from the mean value.

Δai
Absolute error of ith observation
ai
ith measured value
amean
Mean value
Mean Absolute Error
Δamean =(Δa1+Δa2+...+Δan)/nΔ\text{amean }= (Δa1 + Δa2 + ... + Δan) / n

Average uncertainty estimated from repeated readings.

Δamean
Mean absolute error
Δa1, Δa2, ..., Δan
Absolute errors
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5

Dimensions & Dimensional Formulae

9 min

Dimensions show how a physical quantity depends on fundamental quantities such as mass, length, time, current and temperature. A dimensional formula expresses this dependence using powers, for example force has dimensional formula [MLT-2]. Units may differ from system to system, but dimensional formula remains the same for a physical quantity. Derived quantities are obtained from formulas using dimensions of base quantities. Some quantities such as strain, refractive index and relative density are dimensionless because they are ratios of similar quantities. Learning common dimensional formulae is extremely useful for NEET because it helps identify quantities, check equations and eliminate wrong options quickly.

Key points6

  • Write formula first, then substitute dimensions of each quantity.
  • Use [M], [L], [T], [A], [K] for mass, length, time, current and temperature.
  • Work, energy and torque have same dimensions [ML2T-2], but they are different physical quantities.
  • Pressure and stress have same dimensions [ML-1T-2].
  • Momentum and impulse have same dimensions [MLT-1].
  • Dimensionless does not always mean unitless in practical naming; radian is a named dimensionless unit.

Memory tricks2

Core Chain: Remember the chain: velocity LT^-1, acceleration LT^-2, force MLT^-2, work ML2T^-2, power ML2T^-3.

Same Dimensions Pair: Momentum = impulse; work = energy = torque; pressure = stress; angular velocity = frequency.

Examples3

Derived Quantity Example

Density = mass/volume = [M]/[L3] = [ML^-3].

Dimensionless Example

Strain = change in length/original length = [L]/[L] = [M0L0T0].

Practice MCQ

Which has dimensions [MLT^-1]? Answer: momentum and impulse.

Common mistakes3

Thinking Same Dimension Means Same Quantity

Work and torque have same dimensions but different physical meanings and vector nature.

Forgetting Area Dimension

Pressure = force/area; area is L2, so pressure is [MLT-2]/[L2] = [ML-1T-2].

Treating All Constants as Dimensionless

G, h and k may be constants but they have dimensions.

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Formulas5

Dimensional Formula
[Q]=[MaLbTcAdKe][Q] = [M^a L^b T^c A^d K^e]

General dimensional expression using fundamental dimensions commonly needed in NEET physics.

Q
Physical quantity
M,L,T,A,K
Mass, length, time, electric current and temperature dimensions
Velocity
v= displacement / timev =\text{ displacement }/\text{ time}
[v]=[LT−1][v] = [LT^-1]

Velocity is rate of change of displacement.

v
Velocity
L,T
Length and time dimensions
Force
F=maF = ma
[F]=[MLT−2][F] = [MLT^-2]

Force is mass multiplied by acceleration.

F
Force
m
Mass
a
Acceleration
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6

Dimensional Analysis & Applications

10 min

Dimensional analysis uses the principle of dimensional homogeneity: in a correct physical equation, every term added or equated must have the same dimensions. This makes it a powerful NEET tool for checking formulas, eliminating wrong options and deriving relations between quantities. For example, the time period of a simple pendulum can be shown to depend on √(l/g), though dimensional analysis cannot find the constant 2π. It can also convert values from one unit system to another using dimensional powers. However, it cannot handle equations involving trigonometric, exponential or logarithmic functions unless their arguments are dimensionless, and it cannot distinguish between quantities with the same dimensions.

Key points6

  • For checking equations, write dimensions of LHS and RHS and compare.
  • For deriving relations, assume Q ∝ a^x b^y c^z and solve powers.
  • For unit conversion, use n2 = n1(M1/M2)^a(L1/L2)^b(T1/T2)^c.
  • Dimensional homogeneity is necessary but not sufficient for correctness.
  • Dimensionless constants such as 2, π and 1/2 are not obtained.
  • NEET options can often be eliminated by checking dimensions only.

Memory tricks2

Homogeneity Rule: Mnemonic: 'Only Same Dimensions Can Sum' — you can add length to length, not length to velocity.

Limitations: Remember 'No CPS': no Constants, no Plus-minus signs, no Same-dimension distinction.

Examples3

Checking Correctness

Check v^2 = u^2 + 2as. v^2 has [L2T^-2]; as has [LT^-2][L] = [L2T^-2]. Hence dimensionally correct.

Deriving Relation

For time period of pendulum, T = k l^x g^y gives x = 1/2 and y = -1/2, so T ∝ √(l/g).

Typical NEET Question

If an option for energy has dimension [MLT^-2], reject it because energy must be [ML2T^-2].

Common mistakes3

Thinking Dimensionally Correct Means Always Correct

s = ut + at^2 is dimensionally correct, but the correct equation has 1/2 before at^2 for uniformly accelerated motion.

Adding Unlike Dimensions

An equation like v = u + at^2 is wrong because at^2 has dimension of length, not velocity.

Forgetting Dimensionless Arguments

In sin(ωt), ωt must be dimensionless; hence ω has dimension T^-1.

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Formulas4

Principle of Homogeneity
[LHS]=[RHS][LHS] = [RHS]

A physically meaningful equation must have same dimensions on both sides.

LHS
Left-hand side of equation
RHS
Right-hand side of equation
Deriving Relation by Dimensions
Q=kaxbyczQ = k a^x b^y c^z

Assume dependence on variables, compare dimensions and solve for powers x, y and z.

Q
Quantity whose relation is to be derived
k
Dimensionless constant not found by dimensional analysis
a,b,c
Relevant physical variables
x,y,z
Unknown powers
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Videos for Units and Measurements

  • Units And Measurements | Complete ChapterUnacademy NEET English · English
  • Class 11 | Units & DimensionsVedantu JEE English · English
  • SI Units and Unit Conversion With Dimensional Analysis | Physics - BasicsPhysics Lab · English
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  • Class 11th – Unit of Measurement | Unit and MeasurementsTutorialsPoint · English
  • UNITS AND DIMENSIONS 03 | Significant Figures & Error Analysis | PhysicsPW English Medium · English
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NEET PYQs from Units and Measurements

The latest 3 of 36 previous-year questions from this chapter.

  1. NEET 2026Set 50MediumQ1

    One main scale division of a Vernier calliper is equal to $1\ \mathrm{mm}$ and the number of divisions on the Vernier scale is 10. When both the jaws touch each other, the Vernier scale shifts to the left of zero of the main scale in such a way that $4^{\text{th}}$ Vernier division coincides with a division of the main scale. If this Vernier calliper measures the length of the wire to be $1\ \mathrm{cm}$, the actual length of the wire is :

    • A$0.60\ \mathrm{cm}$
    • B$0.96\ \mathrm{cm}$
    • C$1.00\ \mathrm{cm}$
    • D$1.04\ \mathrm{cm}$

  2. NEET 2026Set 50MediumQ2

    Consider that $\sigma_s$, $k_B$, $b$ represents Stefan-Boltzmann constant, Boltzmann constant and Wien’s displacement law constant, respectively. The dimension of $\sigma_s k_B^{-1} b$ is

    • A$[\mathrm{L^{-1}T^{-1}K^{-2}}]$
    • B$[\mathrm{L^{-1}K^{-2}}]$
    • C$[\mathrm{L^{-1}T^{-1}K^{-3}}]$
    • D$[\mathrm{L^{-1}T^{-1}K^{-4}}]$

  3. NEET 2026Set 11MediumQ3

    In a vernier caliper, 20 VSD coincide with 16 MSD (each division length 1 mm). The least count of the vernier calipers is:

    • A0.2 cm
    • B0.01 cm
    • C0.02 cm
    • D0.1 cm
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