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Physics and Measurement – JEE Main Physics Formula Sheet & Class 11 Notes | Units, Dimensions, Errors, Significant Figures & All Measurement Formulas
This is the complete JEE Main Physics Formula Sheet and Class 11 Formula Sheet for Physics and Measurement — Chapter 01 from the Aakash Rapid Revision & Formula Bank. Physics and Measurement is the foundational chapter of all JEE Main Physics. It covers: Physical Quantities — fundamental (base) and derived; SI System — 7 base units (metre, kilogram, second, ampere, kelvin, candela, mole) with symbols; Supplementary Units — radian and steradian; SI Prefixes — from atto (10⁻¹⁸) to exa (10¹⁸); Dimensions — dimensional formula [MᵃLᵇTᶜ] for all major physical quantities; Dimensional Analysis — checking correctness of equations, deriving relations, converting units between systems using n₁u₁=n₂u₂; Significant Figures — 6 rules for counting, 2 rules for rounding, rules for arithmetic operations; Errors in Measurement — mean absolute error Δa, relative error Δa/aₘ, percentage error (Δa/aₘ)×100%, and Combination of Errors — sum/difference (errors add), product/quotient (fractional errors add), power law (fractional error multiplies by exponent). Physics and Measurement contributes 2–3 questions in every JEE Main session. Download the Free PDF for all Physics and Measurement formulas and dimensional tables in one JEE Main exam-ready reference.
Topics Covered in This Physics and Measurement Formula Sheet
Physics and Measurement JEE Main Formula Sheet PDF Preview
Scroll to explore all Physics and Measurement formulas — JEE Main Physics Formula Sheet
Introduction: Why Physics and Measurement Is the Foundation of All JEE Main Physics
Physics and Measurement is not just the first chapter of JEE Main Physics — it is the language in which all other chapters are written. Every physical law, every formula, every numerical answer in JEE Main physics is expressed in units. Understanding dimensional analysis means you can check whether a derived formula is correct, derive unknown relations, and convert between unit systems — skills that are used in every chapter from Mechanics to Modern Physics. Understanding errors in measurement means you can answer any experimental-data question in JEE Main with complete confidence.
For JEE Main physics, Physics and Measurement contributes 2–3 questions per session. These questions test: dimensional formulas of given quantities, checking dimensional correctness of equations, error propagation in power-law formulas (ΔZ/Z = p·ΔA/A + q·ΔB/B + r·ΔC/C), significant figures in arithmetic, and Vernier callipers/screw gauge least count calculations. Every question in Physics and Measurement is a direct formula-application question — no conceptual ambiguity, pure substitution.
Download the Free PDF for Physics and Measurement to access all 7 SI base unit definitions, complete dimensional formula table (30+ quantities), all significant figure rules, all error combination formulas, and instrument least count formulas in one structured JEE Main physics revision reference.
Key Concepts and Formulas in Physics and Measurement
Physical Quantities, SI Units, and the n × u = constant Relation
Why the 7 Base SI Units and the n×u Relation Are the Starting Point of All Physics and Measurement JEE Main Formulas
Physical Quantities (from Aakash PDF — Physics and Measurement):
A physical quantity is any quantity that can be measured. Every physical quantity = numerical value × unit: Q = n × u. Key relation: n × u = constant. This means the numerical value (n) is inversely proportional to the size of the unit (u). If you express 1 metre in centimetres, n increases; if you express in kilometres, n decreases.
Physical quantities are classified as:
Fundamental (Base) Quantities: Treated as independent; defined without reference to other physical quantities. There are 7 base quantities.
Derived Quantities: Expressed as combinations of base quantities. Example: velocity = length/time → derived from length and time.
The 7 SI Base Units (from Aakash PDF — Physics and Measurement JEE Main):
(1) Length — metre (m)
(2) Mass — kilogram (kg)
(3) Time — second (s)
(4) Electric Current — ampere (A)
(5) Thermodynamic Temperature — kelvin (K)
(6) Luminous Intensity — candela (cd)
(7) Amount of Substance — mole (mol)
Supplementary Units (Physics and Measurement — JEE Main):
Plane angle — radian (rad); Solid angle — steradian (sr). These are dimensionless units.
Unit Systems (from Aakash PDF — Physics and Measurement):
CGS system: centimetre (cm), gram (g), second (s). FPS system: foot (ft), pound (lb), second (s). MKS system: metre (m), kilogram (kg), second (s). SI system: modernised and extended form of MKS — the current international standard. SI is a decimal (metric) system.
SI Prefixes (Physics and Measurement — JEE Main):
atto (a) = 10⁻¹⁸; femto (f) = 10⁻¹⁵; pico (p) = 10⁻¹²; nano (n) = 10⁻⁹; micro (μ) = 10⁻⁶; milli (m) = 10⁻³; centi (c) = 10⁻²; deci (d) = 10⁻¹; deca (da) = 10¹; hecto (h) = 10²; kilo (k) = 10³; mega (M) = 10⁶; giga (G) = 10⁹; tera (T) = 10¹²; peta (P) = 10¹⁵; exa (E) = 10¹⁸.
Unit symbol rules (from Aakash PDF — Physics and Measurement): Symbols are not followed by a full stop. Unit symbols are never used in plural form (100 m not 100 ms). Not more than one solidus (/) in a unit symbol — m/s² correct; m/s/s incorrect. Download the Free PDF for Physics and Measurement for all unit definitions and conversion examples for JEE Main.
Dimensions and Dimensional Formulas — Complete Table
Why the Dimensional Formula Table Is the Most-Referenced Physics and Measurement JEE Main Resource
Dimensions of Physical Quantities (from Aakash PDF — Physics and Measurement):
All physical quantities expressed in derived units can be written in terms of combinations of the 7 fundamental quantities (dimensions). These 7 dimensions are denoted with square brackets: [M] = mass, [L] = length, [T] = time, [A] = electric current (ampere), [θ] or [K] = temperature, [cd] = luminous intensity, [N] or [mol] = amount of substance.
The dimensional formula of a quantity: [Q] = [Mᵃ Lᵇ Tᶜ Aᵈ θᵉ] where a,b,c,d,e are dimensional exponents (can be positive, negative, fractional, or zero).
Complete Dimensional Formula Table (from Aakash PDF — Physics and Measurement JEE Main):
Mechanics — Basic Quantities:
Velocity: [M⁰LT⁻¹]
Acceleration: [M⁰LT⁻²]
Force (F = ma): [MLT⁻²]
Momentum (p = mv): [MLT⁻¹]
Work/Energy (W = Fs): [ML²T⁻²]
Power (P = W/t): [ML²T⁻³]
Pressure/Stress (F/A): [ML⁻¹T⁻²]
Angular momentum (L = mvr): [ML²T⁻¹]
Torque (τ = Fr): [ML²T⁻²]
Moment of Inertia (I = mr²): [ML²]
Surface tension (F/l): [MT⁻²]
Coefficient of viscosity (η): [ML⁻¹T⁻¹]
Gravitational constant (G): [M⁻¹L³T⁻²]
Spring constant (k): [MT⁻²]
Thermodynamics:
Heat capacity / Boltzmann constant (k_B): [ML²T⁻²K⁻¹]
Specific heat capacity: [M⁰L²T⁻²K⁻¹]
Stefan's constant (σ): [MT⁻³K⁻⁴]
Thermal conductivity (K): [MLT⁻³K⁻¹]
Electromagnetism (from Aakash PDF — Physics and Measurement):
Absolute permittivity (ε₀): [M⁻¹L⁻³T⁴A²]
Absolute permeability (μ₀): [MLT⁻²A⁻²]
Resistance (R = V/I): [ML²T⁻³A⁻²]
Inductance (L): [ML²T⁻²A⁻²]
Capacitance (C): [M⁻¹L⁻²T⁴A²]
Charge (q = It): [AT]
Electric potential/EMF (V = W/q): [ML²T⁻³A⁻¹]
Electric field (E = F/q): [MLT⁻³A⁻¹]
Magnetic field (B): [MT⁻²A⁻¹]
Magnetic flux (Φ = BA): [ML²T⁻²A⁻¹]
Important dimensionless quantities in Physics and Measurement:
Plane angle (radian), strain, relative density, refractive index, coefficient of friction, Poisson's ratio, fine structure constant — all are [M⁰L⁰T⁰] = dimensionless.
Quantities with same dimensions (Physics and Measurement — JEE Main):
[ML²T⁻²]: Work, energy, torque, heat (all same dimensions). [ML⁻¹T⁻²]: Pressure, stress, Young's modulus, bulk modulus, energy density, B²/2μ₀, ε₀E²/2. [MLT⁻¹]: Linear momentum, impulse. [ML²T⁻¹]: Angular momentum, Planck's constant (h). [MT⁻²]: Surface tension, spring constant. Time constants [M⁰L⁰T]: RC = time constant of RC circuit; L/R = time constant of LR circuit; √(LC) = [T]. [M⁰L⁰T⁻¹]: 1/√(ε₀μ₀) = speed of light (c).
Download the Free PDF for Physics and Measurement for the complete dimensional formula table with useful results for JEE Main.
Dimensional Analysis — All 3 Uses and Unit Conversion Formula
Why Dimensional Analysis Is the Most Versatile Physics and Measurement Tool in JEE Main
Principle of Homogeneity of Dimensions (from Aakash PDF — Physics and Measurement):
Every term in a physically correct equation must have the same dimensions. If any term in an equation has different dimensions, the equation is dimensionally incorrect — and therefore physically wrong.
Dimensionless functions like sin, cos, log, exponential must always have dimensionless arguments. So in e^(–t/τ): the exponent t/τ must be dimensionless → τ must have dimensions of time.
Use 1 — Checking Dimensional Correctness of Equations (from Aakash PDF — Physics and Measurement JEE Main):
Method: Find dimensions of every term on both sides of the equation. If all terms have the same dimensions → equation is dimensionally correct (may still be wrong by a dimensionless constant). If any term has different dimensions → equation is definitely wrong.
Example: v = u + at → [v]=LT⁻¹; [u]=LT⁻¹; [at]=[LT⁻²·T]=LT⁻¹ ✓ — all terms same → dimensionally correct.
Use 2 — Deriving Relations Using Dimensional Analysis (from Aakash PDF — Physics and Measurement JEE Main):
If a physical quantity Q depends on quantities A, B, C: assume Q = k·Aᵃ·Bᵇ·Cᶜ. Write dimensions of both sides. Set up simultaneous equations by matching exponents of M, L, T. Solve for a, b, c. Determine Q up to a dimensionless constant k (which must be found experimentally or by other methods).
Example: Time period T of simple pendulum depends on length l and g. Let T = k·lᵃ·gᵇ. [T] = [L]ᵃ[LT⁻²]ᵇ → T¹ = Lᵃ⁺ᵇ T⁻²ᵇ → a+b=0 and –2b=1 → b=–½, a=½. So T = k√(l/g) = 2π√(l/g). Note: dimensional analysis gives the form but NOT the constant 2π.
Use 3 — Conversion of Units Between Systems (from Aakash PDF — Physics and Measurement JEE Main):
If a quantity has dimensional formula [MᵃLᵇTᶜ], and the unit sizes in system 1 are M₁, L₁, T₁ and in system 2 are M₂, L₂, T₂:
n₂ = n₁ × (M₁/M₂)ᵃ × (L₁/L₂)ᵇ × (T₁/T₂)ᶜ
This converts the numerical value n₁ in system 1 to n₂ in system 2 (since n₁u₁ = n₂u₂).
Example: Convert 1 joule to CGS units (erg). Joule = [ML²T⁻²]. n₁=1, M₁=1kg=1000g, L₁=1m=100cm, T₁=1s=1s, M₂=1g, L₂=1cm, T₂=1s. n₂ = 1×(1000/1)¹×(100/1)²×(1/1)⁻² = 1000×10000 = 10⁷. So 1 J = 10⁷ erg.
Limitations of Dimensional Analysis (Physics and Measurement — JEE Main):
(1) Cannot determine dimensionless constants (like 2π in pendulum period, ½ in kinetic energy).
(2) Cannot determine if an equation has a sum/difference of terms with same dimensions.
(3) Does not work for exponential, logarithmic, or trigonometric relations.
(4) Cannot distinguish between physical quantities that have the same dimensional formula (e.g., work and torque both [ML²T⁻²]). Download the Free PDF for Physics and Measurement for all dimensional analysis examples and conversion problems for JEE Main.
Accuracy, Precision, and Significant Figures — All Rules
Why Significant Figure Rules Are Direct Physics and Measurement JEE Main Questions
Accuracy vs Precision (from Aakash PDF — Physics and Measurement):
Accuracy: How close a measurement is to the true (actual) value. The measurement with minimum deviation from the true value is most accurate.
Precision: How reproducible successive measurements are — how many decimal places the measurement is expressed to. More decimal places = more precise (regardless of true value).
Example from PDF: True value = 35.75. Measurements: 35.73 and 35.725. 35.73 is more accurate (closer to 35.75). 35.725 is more precise (expressed to 3 decimal places vs 2 decimal places). Accuracy and precision are independent concepts — a measurement can be precise but inaccurate.
Significant Figures — Definition (from Aakash PDF — Physics and Measurement): The number of digits in a measured value about the correctness of which we are sure PLUS one more digit (the last, uncertain digit). More significant figures = more precise measurement.
6 Rules for Counting Significant Figures (from Aakash PDF — Physics and Measurement JEE Main):
Rule I: All non-zero digits are significant. Example: 2356 has 4 significant figures.
Rule II: All zeros occurring between two non-zero digits are significant. Example: 230089 has 6 significant figures (0, 0 between 3 and 8, and 8, 9).
Rule III: All zeros to the left of the first non-zero digit are NOT significant (leading zeros). Example: 0.0023 has 2 significant figures (only 2 and 3); 0.00420 needs further rule.
Rule IV: If a number ends in zeros that are NOT to the right of a decimal point, the zeros may or may not be significant (ambiguous). Example: 23400 could have 3, 4, or 5 significant figures — use scientific notation to remove ambiguity (2.34×10⁴ = 3 SF; 2.340×10⁴ = 4 SF).
Rule V: Trailing zeros after a decimal point ARE significant. Example: 23.400 has 5 significant figures.
Rule VI: Pure (exact) numbers and defined constants have infinite significant figures. Example: the "2" in d = 2r; π; exact whole numbers in counting. Download the Free PDF for Physics and Measurement for all significant figure examples for JEE Main.
Rounding Rules (from Aakash PDF — Physics and Measurement JEE Main):
Rule I: If the digit to be dropped is greater than 5 — raise the preceding digit by 1. Example: 7.36 rounded to 1 decimal → 7.4.
Rule II: If the digit to be dropped is exactly 5 — apply the even-odd rule: if the preceding digit is even, simply drop the 5; if odd, raise the preceding digit by 1. Example: 4.35 → 4.4 (3 is odd → raise); 4.25 → 4.2 (2 is even → simply drop).
Significant Figures in Arithmetic Operations (Physics and Measurement — JEE Main):
Addition and Subtraction: The result should retain as many DECIMAL PLACES as the term with the fewest decimal places. Example: 23.01 + 37.3 = 60.31 → round to 1 decimal → 60.3 (because 37.3 has only 1 decimal place).
Multiplication and Division: The result should retain as many SIGNIFICANT FIGURES as the original number with the fewest significant figures. Example: 4.0 × 3.25 = 13.00 → round to 2 SF → 13 (because 4.0 has 2 SF).
Errors in Measurement — All Formulas and Combination Rules
Why Error Propagation Formulas Are the Highest-Scoring Physics and Measurement Topics in JEE Main
Types of Errors (from Aakash PDF — Physics and Measurement):
Systematic errors: Errors that affect every measurement in a consistent direction (always too high or always too low). Sources: instrument errors (zero error, calibration), personal errors, environmental errors. Can be corrected once identified.
Random errors: Errors that vary unpredictably in magnitude and direction from measurement to measurement. Reduced by taking multiple measurements and averaging.
Gross errors (blunders): Mistakes made by the observer — reading wrong scale, recording wrong value.
Mean Absolute Error (from Aakash PDF — Physics and Measurement JEE Main):
If n measurements of a quantity give values a₁, a₂, a₃, …, aₙ:
True value (mean): aₘ = (a₁ + a₂ + … + aₙ) / n
Absolute errors: Δa₁ = aₘ – a₁; Δa₂ = aₘ – a₂; …; Δaₙ = aₘ – aₙ
Mean absolute error: Δa = (|Δa₁| + |Δa₂| + … + |Δaₙ|) / n
Final result: a = aₘ ± Δa
Relative Error (Fractional Error) (from Aakash PDF — Physics and Measurement):
Relative error = Δa / aₘ = Mean absolute error / Mean value
Percentage Error (from Aakash PDF — Physics and Measurement JEE Main):
Percentage error = (Δa / aₘ) × 100%
Example: screw gauge reading = 0.802 cm, least count = 0.001 cm. Percentage error = (0.001/0.802)×100% = 0.125%.
Combination of Errors — Sum and Difference (from Aakash PDF — Physics and Measurement JEE Main):
If Z = A + B or Z = A – B: ΔZ = ΔA + ΔB
The maximum absolute error in the sum or difference is the SUM of the absolute errors. (When quantities are added or subtracted, their absolute errors always add.)
Fractional error in this case: ΔZ/Z = (ΔA + ΔB)/(A ± B)
Combination of Errors — Product and Quotient (from Aakash PDF — Physics and Measurement JEE Main):
If Z = A × B or Z = A / B: ΔZ/Z = ΔA/A + ΔB/B
The maximum fractional (relative) error in the product or quotient is the SUM of the fractional errors. (When quantities are multiplied or divided, their fractional errors add.)
Combination of Errors — Power Law (from Aakash PDF — Physics and Measurement JEE Main):
If Z = Aᵖ · Bq / Cʳ: ΔZ/Z = p·(ΔA/A) + q·(ΔB/B) + r·(ΔC/C)
The fractional error in the result is the sum of (exponent × fractional error) for each quantity.
Example: If P = V²/R, ΔP/P = 2·ΔV/V + ΔR/R.
Example: Percentage error in R = V/I: %R = %V + %I = 3% + 2% = 5%.
Example: If T = 2π√(l/g): ΔT/T = ½·Δl/l + ½·Δg/g.
General formula: if Z = (Aᵃ·Bᵇ)/(Cᶜ·Dᵈ): ΔZ/Z = a·ΔA/A + b·ΔB/B + c·ΔC/C + d·ΔD/D. Download the Free PDF for Physics and Measurement for all error combination examples for JEE Main.
Measuring Instruments — Vernier Callipers and Screw Gauge
Why Least Count Formulas and Vernier/Screw Gauge Reading Are Direct Physics and Measurement JEE Main Questions
Least Count (from Aakash PDF — Physics and Measurement JEE Main): The least count of a measuring instrument is the smallest value that can be measured (or the smallest change that can be detected) by that instrument. Error in measurement cannot be less than the least count.
Percentage error in any measurement = (Least Count / Measured Value) × 100%.
Vernier Callipers (Physics and Measurement — JEE Main):
A Vernier calliper has a main scale (MS) and a Vernier scale (VS). The Vernier scale has n divisions that equal (n–1) main scale divisions.
Least Count of Vernier Calliper = 1 MSD – 1 VSD = 1 MSD – (n–1)/n MSD = (1/n) MSD
Or: LC = 1 MSD – 1 VSD (the difference between one main scale division and one Vernier scale division).
Standard: if 10 VS divisions = 9 MS divisions → 1 VSD = 0.9 MSD → LC = 1 – 0.9 = 0.1 mm = 0.01 cm.
Reading from Vernier Calliper:
Total reading = Main scale reading + (Vernier scale division that coincides × Least Count)
Total reading = MSR + n × LC
Zero Error in Vernier Calliper: Positive zero error → subtract from reading. Negative zero error → add to reading. Corrected reading = Observed reading – Zero error.
Screw Gauge (Physics and Measurement — JEE Main):
A screw gauge has a main scale (pitch scale) and a circular scale (thimble scale).
Pitch = distance moved by screw per complete rotation = distance between adjacent main scale divisions.
Least Count of Screw Gauge = Pitch / Total number of circular scale divisions
Standard: Pitch = 1 mm, Circular divisions = 100 → LC = 1/100 mm = 0.01 mm = 0.001 cm.
Reading from Screw Gauge:
Total reading = Main scale reading + (Circular scale reading × Least Count)
Total reading = MSR + CSR × LC
Backlash error: Due to loose fitting of screw — always move the screw in one direction during measurement.
Zero Error in Screw Gauge: If circular scale zero line is above reference line → negative zero error → add the magnitude. If below → positive zero error → subtract. Download the Free PDF for Physics and Measurement for all Vernier and screw gauge problems for JEE Main.
Download Free PDF — Physics and Measurement JEE Main Formula Sheet
All Physics and Measurement formulas from the Aakash Rapid Revision PDF: physical quantities (fundamental and derived), n×u=constant, all 7 SI base units (m/kg/s/A/K/cd/mol) with symbols, supplementary units (radian, steradian), CGS/FPS/MKS/SI systems, all SI prefixes (10⁻¹⁸ to 10¹⁸), 7 dimensions [M L T A θ cd N], complete dimensional formula table (velocity [LT⁻¹], acceleration [LT⁻²], force [MLT⁻²], momentum [MLT⁻¹], work/energy/torque [ML²T⁻²], power [ML²T⁻³], pressure/stress/energy density [ML⁻¹T⁻²], angular momentum = Planck's constant h [ML²T⁻¹], surface tension = spring constant [MT⁻²], coefficient of viscosity [ML⁻¹T⁻¹], gravitational constant [M⁻¹L³T⁻²], resistance [ML²T⁻³A⁻²], inductance [ML²T⁻²A⁻²], capacitance [M⁻¹L⁻²T⁴A²], permittivity [M⁻¹L⁻³T⁴A²], permeability [MLT⁻²A⁻²], charge [AT], potential [ML²T⁻³A⁻¹], magnetic field [MT⁻²A⁻¹], Boltzmann constant [ML²T⁻²K⁻¹], RC=L/R=[T], dimensionless quantities), principle of homogeneity, 3 uses of dimensional analysis (check/derive/convert), unit conversion n₂=n₁(M₁/M₂)ᵃ(L₁/L₂)ᵇ(T₁/T₂)ᶜ, 4 limitations of dimensional analysis, accuracy vs precision, 6 rules for significant figures, 2 rounding rules (even-odd for =5), SF in addition/subtraction (decimal places), SF in multiplication/division (significant figures), mean absolute error Δa=Σ|Δaᵢ|/n, result aₘ±Δa, relative error Δa/aₘ, percentage error (Δa/aₘ)×100%, error in sum/difference ΔZ=ΔA+ΔB, error in product/quotient ΔZ/Z=ΔA/A+ΔB/B, general power-law error ΔZ/Z=p·ΔA/A+q·ΔB/B+r·ΔC/C, Vernier LC=1MSD–1VSD, Vernier reading=MSR+n×LC, screw gauge LC=Pitch/divisions, screw gauge reading=MSR+CSR×LC, zero error correction.
Why Physics and Measurement Is a Cross-Chapter Tool for JEE Main Physics
Dimensional analysis is the universal error-checking method across all JEE Main physics chapters. In Mechanics, checking v²=u²+2as; in Electromagnetism, checking E=hν; in Thermodynamics, checking PV=nRT — the same method applies. Every time JEE Main gives "which of the following equations is dimensionally correct?" it is testing the principle of homogeneity from Physics and Measurement Chapter 1.
The error propagation formula ΔZ/Z = p·ΔA/A + q·ΔB/B + r·ΔC/C is the single most-tested Physics and Measurement formula in JEE Main. It appears whenever experimental data is involved: "If P = V²/R and errors in V and R are 2% and 1% respectively, find the percentage error in P." Answer: ΔP/P = 2·ΔV/V + ΔR/R = 2×2% + 1% = 5%. This formula reduces every error combination question to simple multiplication and addition.
Knowing dimensional formulas of all major quantities makes JEE Main numerical problems faster. If you know [h] = [ML²T⁻¹] = [angular momentum], then h/(2π) has dimensions of angular momentum — so Planck's constant divided by angular frequency gives energy [ML²T⁻²]. These cross-links between Physical Measurement dimensional formulas and other chapters create shortcuts throughout JEE Main physics.
Vernier callipers and screw gauge reading questions follow a fixed 3-step algorithm. (1) Read main scale. (2) Find which Vernier/circular division coincides with the main scale. (3) Add (coinciding division × LC) to main scale reading. Apply zero error correction. Every instrument-reading question in JEE Main follows this identical algorithm. Download the Free PDF for Physics and Measurement to have all formulas ready.
Who Should Use This Physics and Measurement Formula Sheet?
Learning Outcomes After Completing Physics and Measurement
After working through Physics and Measurement using this formula sheet, a student should confidently accomplish the following for JEE Main physics. On units: name all 7 SI base units and their symbols; state 2 supplementary units; name SI prefixes and their powers from 10⁻¹⁸ to 10¹⁸; convert units using n₁u₁=n₂u₂ and the general conversion formula n₂=n₁(M₁/M₂)ᵃ(L₁/L₂)ᵇ(T₁/T₂)ᶜ.
On dimensions: write the dimensional formula [MᵃLᵇTᶜ] for any standard physical quantity; identify dimensionless quantities; identify pairs of quantities with the same dimensional formula; use the principle of homogeneity to check whether a given equation is dimensionally correct; derive a physical relation using dimensional analysis given the dependencies; state all 4 limitations of dimensional analysis.
On significant figures: apply all 6 rules to count significant figures in any given number; round correctly using the even-odd rule for the =5 case; express results of addition/subtraction to the correct number of decimal places; express results of multiplication/division to the correct number of significant figures.
On errors: compute mean absolute error Δa from repeated measurements; express the result as aₘ±Δa; compute relative and percentage errors; apply the error combination rule for sums/differences (absolute errors add); apply the error combination rule for products/quotients (fractional errors add); apply the general power-law error formula ΔZ/Z=p·ΔA/A+q·ΔB/B+r·ΔC/C; calculate least count of Vernier callipers and screw gauge; read and correct for zero error. Download the Free PDF for Physics and Measurement to test all outcomes before your JEE Main exam.
Get the Free PDF for Physics and Measurement — JEE Main Quick Revision
The Aakash Rapid Revision & Formula Bank PDF for Physics and Measurement contains all SI unit definitions, complete dimensional formula table, dimensional analysis methods, unit conversion formula, all significant figure rules, all error combination formulas, and instrument least count formulas in one compact JEE Main physics reference.
Conclusion — Physics and Measurement: The Foundation Layer of JEE Main Physics
Physics and Measurement is the chapter that makes all other JEE Main physics questions solvable with confidence. Understanding that every physical quantity has a precise unit and a dimensional formula means you can check any formula, convert any unit, and estimate any error — not just in Physics and Measurement questions, but in every other chapter.
The three pillars of Physics and Measurement for JEE Main: (1) Dimensional formulas — memorise the table, especially the electromagnetic quantities (resistance, capacitance, inductance, permittivity, permeability) which are highest-difficulty items; (2) Error combination — the power-law formula ΔZ/Z=p·ΔA/A+q·ΔB/B is the single most-tested formula; (3) Significant figures — the addition/subtraction rule (decimal places) and multiplication/division rule (significant figures) are the two most-tested SF results. Master these three pillars from this page and the Free PDF Download for Physics and Measurement, and guarantee 8–12 marks across all JEE Main physics sessions.
Frequently Asked Questions — Physics and Measurement Formulas
What are the 7 SI base units in Physics and Measurement?
In Physics and Measurement, the 7 SI base units are: (1) Length — metre (m): defined as the distance light travels in vacuum in 1/299,792,458 seconds. (2) Mass — kilogram (kg): defined in terms of Planck's constant h=6.626×10⁻³⁴ J·s. (3) Time — second (s): defined as 9,192,631,770 periods of radiation from caesium-133 atom. (4) Electric current — ampere (A). (5) Thermodynamic temperature — kelvin (K). (6) Luminous intensity — candela (cd). (7) Amount of substance — mole (mol). Two supplementary units: radian (rad) for plane angle; steradian (sr) for solid angle. All other physics units (newton, joule, watt, pascal, volt, ohm, farad, henry, tesla, etc.) are derived from these 7 base units. The relation n×u=constant means the numerical value is inversely proportional to the unit size — expressing 1 metre in centimetres gives 100 (larger numerical value, smaller unit). These Physics and Measurement base unit facts are directly tested in JEE Main.
What is the dimensional formula of resistance, capacitance, and inductance in Physics and Measurement?
In Physics and Measurement, the electromagnetic dimensional formulas from the Aakash PDF: Resistance R=V/I=W/(I²t): [R]=[ML²T⁻³A⁻²]. Derivation: R=V/I=[ML²T⁻³A⁻¹]/[A]=[ML²T⁻³A⁻²]. Capacitance C=q/V=[AT]/[ML²T⁻³A⁻¹]=[M⁻¹L⁻²T⁴A²]. Inductance L from energy U=½LI²: [L]=[U/I²]=[ML²T⁻²]/[A²]=[ML²T⁻²A⁻²]. Time constants: τ_RC=RC → [M⁻¹L⁻²T⁴A²][ML²T⁻³A⁻²]=[T] ✓. τ_LR=L/R → [ML²T⁻²A⁻²]/[ML²T⁻³A⁻²]=[T] ✓. √(LC): [ML²T⁻²A⁻²]^½ × [M⁻¹L⁻²T⁴A²]^½ = [T] ✓. Permittivity ε₀: from F=q²/(4πε₀r²) → [ε₀]=[q²/Fr²]=[A²T²]/([MLT⁻²][L²])=[M⁻¹L⁻³T⁴A²]. Permeability μ₀: from F=μ₀I²l/(2πr) → [μ₀]=[MLT⁻²]/[A²]=[MLT⁻²A⁻²]. Magnetic field B (from F=qvB): [B]=[F/(qv)]=[MLT⁻²]/([AT][LT⁻¹])=[MT⁻²A⁻¹]. These Physics and Measurement electromagnetic dimensions are the most frequently asked in JEE Main dimensional analysis questions.
How is dimensional analysis used to derive relations and convert units in Physics and Measurement?
In Physics and Measurement, dimensional analysis has 3 main uses: Use 1 (Check correctness): apply the principle of homogeneity — all terms in a correct equation must have the same dimensions. Use 2 (Derive relations): assume Q=k·Aᵃ·Bᵇ·Cᶜ → write dimensional equation → equate powers of M, L, T → solve for a, b, c → the dimensionless constant k cannot be found. Example: time period of pendulum T depends on l and g. T=k·lᵃ·gᵇ → T¹=[L]ᵃ[LT⁻²]ᵇ → a+b=0 and -2b=1 → a=½, b=-½ → T=k√(l/g)=2π√(l/g) (k=2π from experiment). Use 3 (Unit conversion): n₂=n₁×(M₁/M₂)ᵃ×(L₁/L₂)ᵇ×(T₁/T₂)ᶜ where a,b,c are dimensions. Example: 1 J in CGS: [J]=[ML²T⁻²]; n₂=1×(1kg/1g)¹×(1m/1cm)²×(1s/1s)⁻²=1000×10000=10⁷. So 1 J=10⁷ erg. Limitations of dimensional analysis in Physics and Measurement: (1) Dimensionless constants unknown; (2) Sum/difference of same-dimensional terms unresolvable; (3) No use for trig/log/exp; (4) Cannot distinguish work from torque (same dimensions).
What are all the significant figure rules in Physics and Measurement?
In Physics and Measurement, the 6 rules for counting significant figures from the Aakash PDF: Rule I: All non-zero digits are significant (3456 → 4 SF). Rule II: Zeros between non-zero digits are significant (230089 → 6 SF; 1007 → 4 SF). Rule III: Leading zeros (before first non-zero digit) are NOT significant (0.0023 → 2 SF; 0.50 → follow Rule V for trailing zero after decimal). Rule IV: Trailing zeros without decimal point are ambiguous (23400 could be 3, 4, or 5 SF — use 2.34×10⁴ to clarify). Rule V: Trailing zeros after decimal point ARE significant (23.400 → 5 SF; 0.050 → 2 SF). Rule VI: Pure/exact/defined numbers have infinite SF (counting number 12 → infinite SF; π → infinite; exact fractions → infinite). Rounding: >5 → raise preceding digit; <5 → drop; =5 → even preceding digit → drop; odd → raise (e.g., 4.35 → 4.4; 4.25 → 4.2). Operations: Addition/subtraction → result has least decimal places of any term (23.01+37.3=60.31→60.3). Multiplication/division → result has least significant figures of any factor (4.0×3.25=13.00→13). These Physics and Measurement SF rules are tested in JEE Main directly.
What is the formula for percentage error in Physics and Measurement?
In Physics and Measurement, the error formulas from the Aakash PDF: Mean value: aₘ=Σaᵢ/n. Absolute errors: Δaᵢ=aₘ–aᵢ. Mean absolute error: Δa=Σ|Δaᵢ|/n. Result: a=aₘ±Δa. Relative (fractional) error: Δa/aₘ. Percentage error: (Δa/aₘ)×100%. Example from PDF: screw gauge reading=0.802 cm, LC=0.001 cm. Percentage error=(0.001/0.802)×100%=0.125%. If only one measurement and instrument LC is known: percentage error=(LC/measured value)×100%. This is the minimum possible percentage error with that instrument. Example: Vernier LC=0.01 cm, measured length=2.5 cm → percentage error=(0.01/2.5)×100%=0.4%. Percentage error in derived quantity: For R=V/I: %R=%V+%I. If %V=3%, %I=2% → %R=5%. For Z=Aᵖ·Bᵍ/Cʳ: %Z=p·%A+q·%B+r·%C. For T=2π√(l/g): %T=½·%l+½·%g. Note: the ABSOLUTE values of exponents are always used — errors always add, never cancel.
How does error propagate in sum, product, and power-law formulas in Physics and Measurement?
In Physics and Measurement, error combination rules from the Aakash PDF: (1) Sum/Difference Z=A+B or Z=A–B: ΔZ=ΔA+ΔB. The maximum absolute error equals the sum of individual absolute errors. For fractional error: ΔZ/Z=(ΔA+ΔB)/(A±B) — note the denominator is A+B or A–B. (2) Product/Quotient Z=A×B or Z=A/B: ΔZ/Z=ΔA/A+ΔB/B. The maximum fractional error equals the sum of individual fractional errors. Percentage: %Z=%A+%B. (3) Power law Z=AᵖBᵍ/Cʳ: ΔZ/Z=|p|·ΔA/A+|q|·ΔB/B+|r|·ΔC/C. Use absolute value of each exponent — powers can be negative, but errors always add. Percentage: %Z=|p|·%A+|q|·%B+|r|·%C. Examples in Physics and Measurement JEE Main: If P=I²R: ΔP/P=2·ΔI/I+ΔR/R. If T=2π√(L/g): ΔT/T=½·ΔL/L+½·Δg/g. If ρ=m/V=m/(πr²h): Δρ/ρ=Δm/m+2·Δr/r+Δh/h. The coefficient (exponent) determines how much each individual error contributes to the final error — hence small errors in quantities with high exponents matter most.
What are the least count formulas for Vernier callipers and screw gauge in Physics and Measurement?
In Physics and Measurement, instrument formulas: Vernier Calliper: Least Count (LC) = 1 Main Scale Division (MSD) – 1 Vernier Scale Division (VSD). Since n VSD = (n–1) MSD, 1 VSD = (n–1)/n × 1 MSD. So LC = 1 MSD – (n–1)/n × 1 MSD = 1/n × 1 MSD. Standard: 10 VSD = 9 MSD, 1 MSD = 1 mm → LC = 0.1 mm = 0.01 cm. Reading: Total = MSR + (coinciding VSD number) × LC. Zero error: if jaws touching shows n divisions on positive side → +n×LC is positive zero error → subtract from all readings. Screw Gauge: LC = Pitch / Total number of circular scale divisions. Pitch = distance moved per complete rotation of thimble. Standard: pitch = 1 mm, divisions = 100 → LC = 0.01 mm. Reading: Total = MSR + (CSR) × LC. Backlash error prevention: always approach measurement from same direction. Reading formula from JEE Advanced 2025 type problem: if VS 10 div = 7 mm and main scale has 1 mm divisions: 1 VSD = 0.7 mm; LC = 1 – 0.7 = 0.3 mm — note non-standard Vernier. These Physics and Measurement instrument formulas are directly tested in JEE Main and Advanced.
Which physical quantities have the same dimensional formula in Physics and Measurement?
In Physics and Measurement, pairs/groups with the same dimensional formula from the Aakash PDF: [ML²T⁻²]: Work, kinetic energy, potential energy, heat, internal energy, torque (same dimensions but different physical meanings — dimensional analysis cannot distinguish them). [ML⁻¹T⁻²]: Pressure, stress, Young's modulus, bulk modulus, shear modulus, energy density (energy/volume), B²/2μ₀ (magnetic energy density), ε₀E²/2 (electric energy density). [MLT⁻¹]: Linear momentum, impulse (Ft). [ML²T⁻¹]: Angular momentum, Planck's constant h. [MT⁻²]: Surface tension, spring constant (force constant). [M⁰L⁰T]: Time constants RC, L/R, √(LC) — all have dimensional formula [T]. [M⁰L⁰T⁻¹]: Angular velocity (ω), frequency (f), decay constant (λ) — all [T⁻¹]. [M⁰L⁰T⁰]: Angle, strain, relative density, refractive index, coefficient of friction — all dimensionless. Knowing these Physics and Measurement groupings prevents errors in dimensional analysis and is directly tested in JEE Main as "which of the following pairs has the same dimensions?"
What are the limitations of dimensional analysis in Physics and Measurement?
In Physics and Measurement, the 4 limitations of dimensional analysis: (1) Cannot determine dimensionless constants: T=2π√(l/g) — the factor 2π cannot be found by dimensions. Similarly, KE=½mv² — the ½ is dimensionless and unknowable from dimensions alone. Any correct equation multiplied by a dimensionless constant is still dimensionally correct. (2) Cannot handle equations with sum/difference of terms with the same dimensions: If Z = A + B where [A]=[B], dimensional analysis cannot verify the equation because all combinations (A+B, A–B, 2A+3B) are dimensionally the same. (3) Not useful for exponential, logarithmic, or trigonometric functions: In e^(–t/RC), sin(ωt), log(P/P₀) — dimensional analysis can only verify that the arguments are dimensionless; the functions themselves are outside its scope. (4) Cannot distinguish between physical quantities with the same dimensions: Work and torque both have [ML²T⁻²]; momentum and impulse both have [MLT⁻¹] — they are dimensionally identical but physically different. An equation mixing work and torque may be dimensionally correct but physically meaningless.
What is the difference between accuracy and precision in Physics and Measurement?
In Physics and Measurement, the distinction from the Aakash PDF: Accuracy is how close a measured value is to the TRUE (actual) value — measured by the magnitude of error (deviation from true value). The measurement with smallest absolute error is most accurate. Precision is how reproducible successive measurements are — measured by the number of significant figures (decimal places). The measurement with more decimal places is more precise. Example from PDF: true value = 35.75. Measurement 1: 35.73. Measurement 2: 35.725. Accuracy: |35.73–35.75|=0.02; |35.725–35.75|=0.025. Measurement 1 is more accurate (smaller deviation from true value). Precision: 35.73 has 2 decimal places; 35.725 has 3 decimal places. Measurement 2 is more precise. Key point in Physics and Measurement: accuracy and precision are independent. A very precise measurement (many decimal places) can be inaccurate (far from true value). Example: a faulty scale giving 10.234 kg consistently when true value is 10.000 kg — precise (4 decimal places) but inaccurate (0.234 kg from true). In JEE Main Physics and Measurement questions, the most precise = most significant figures; the most accurate = closest to true value.
Related Formula Sheets — JEE Main Physics
Physics and Measurement – JEE Main Physics Formula Sheet
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