Units, Measurements & Dimensional Analysis – Class 11 Physics

Vocabulary flashcards covering major terms and definitions from the Class 11 ‘Units and Measurements’ lecture, including units, dimensional analysis, significant figures, error analysis, measuring instruments, and related rules.

Physical Quantity

A measurable property of a material or system that can be expressed numerically with a unit (e.g., mass, length).

Numerical Value (of a measurement)

The magnitude of a physical quantity expressed as a pure number, preceding the unit.

Unit

An internationally accepted standard used to express physical quantities (e.g., metre, kilogram).

Equation of a Physical Quantity

Physical Quantity = Numerical Value × Unit.

Fundamental Unit

A base unit that is independent and cannot be derived from other units (e.g., metre, kilogram, second).

Number of SI Base Units

Seven: metre, kilogram, second, ampere, kelvin, mole, candela.

Derived Unit

A unit obtained by combining fundamental units (e.g., m s⁻¹ for velocity).

SI System

International System of Units comprising seven base units and derived units; globally accepted for science and technology.

FPS System

Foot–Pound–Second system of units, once common in engineering (US).

CGS System

Centimetre–Gram–Second system, historically used in small-scale measurements.

MKS System

Metre–Kilogram–Second system, precursor to the SI.

Supplementary Quantity

Geometrical quantity not classed as fundamental or derived; used for angles (plane & solid).

Plane Angle

Angle between two intersecting lines; SI unit radian (rad).

Solid Angle

Three-dimensional angle subtended by a surface at a point; SI unit steradian (sr).

Inverse Relation of n and u

For a constant physical quantity, numerical value n ∝ 1/unit u (n u = constant).

Prefix (in SI)

A factor used to form decimal multiples/submultiples of units (e.g., kilo-, milli-).

Dimension (of a quantity)

Power to which base quantities are raised to represent the quantity (e.g., [M¹L¹T⁻²] for force).

Dimensional Formula

Expression of a quantity in terms of fundamental dimensions, e.g., [M¹L¹T⁻²] for force.

Principle of Homogeneity

An equation is dimensionally correct only if each term has identical dimensions on both sides.

Dimensionless Quantity

A quantity whose dimensional formula is [M⁰L⁰T⁰]; often a ratio (e.g., strain, refractive index).

Impulse

Product of force and time interval; dimension [M¹L¹T⁻¹].

Stress

Force per unit area; dimension [M¹L⁻¹T⁻²].

Strain

Ratio of change in length to original length; dimensionless.

Gravitational Constant (G)

Constant in Newton’s law of gravitation; dimension [M⁻¹L³T⁻²].

Surface Tension

Force per unit length; dimension [M¹T⁻²].

Planck’s Constant (h)

Proportionality constant in E = hν; dimension [M¹L²T⁻¹].

Universal Gas Constant (R)

Constant in PV = nRT; dimension [M¹L²T⁻²K⁻¹mol⁻¹].

Principle Use of Dimensional Analysis

Checking equations, deriving relations, converting units, estimating magnitudes.

Limitation of Dimensional Analysis

Cannot give numerical constants; fails for trigonometric/exponential relations; ignores vector nature.

Significant Figures

Digits in a number that convey meaningful measurement information.

Rule 1 (Non-zero digits)

All non-zero digits are significant.

Rule 2 (Zeros between non-zeros)

Zeros between significant digits are significant.

Leading Zeros

Zeros preceding first non-zero digit; not significant.

Trailing Zeros with Decimal

Zeros after a decimal point are significant.

Trailing Zeros without Decimal

Zeros at end of whole number without decimal are not significant.

Exact Number

Counted/defined value with infinite significant figures (e.g., 12 eggs).

Scientific Notation & S.F.

All digits in coefficient a of a × 10ⁿ are significant; exponent digits are not.

Rounding (<5)

If dropped digit <5, preceding digit unchanged.

Rounding (>5)

If dropped digit >5, preceding digit raised by one.

Rounding (5 followed by zeros)

If preceding digit even, unchanged; if odd, raised by one.

Addition/Subtraction Rule (S.F.)

Result keeps as many decimal places as the least precise addend.

Multiplication/Division Rule (S.F.)

Result keeps as many significant figures as the factor with fewest S.F.

Least Count

Smallest value that an instrument can measure accurately.

Screw Gauge

Precision device using a screw to measure small lengths (accuracy ~0.01 mm).

Pitch (Screw Gauge)

Linear distance advanced per one complete rotation of the screw.

Vernier Caliper

Instrument measuring internal/external dimensions & depth with 0.1 mm or 0.01 cm precision.

Vernier Reading Formula

Observed length = MSR + (VSD × Least Count).

Error (General)

Difference between measured and true value of a quantity.

Absolute Error

Magnitude of (measured – true) value; always positive.

Relative Error

Absolute error divided by true value; dimensionless fraction.

Percentage Error

Relative error × 100 %.

Propagation of Errors (Add/Sub)

Absolute errors add: ΔZ = ΔA + ΔB, even if Z = A ± B.

Propagation of Errors (Mult/Div)

Relative errors add: ΔZ/Z = ΔA/A + ΔB/B for Z = A × B or A/B.

Error in Power Function

For Z = Aⁿ, relative error in Z = |n| × (ΔA/A).

Systematic Error

Consistent bias in measurement; affects accuracy but can be corrected.

Random Error

Unpredictable variations in repeated measurements; affects precision.

Total Surface Area of Cube (formula)

A = 6a², where a is side length.

Volume of Cube (formula)

V = a³.

Mean Value (of measurements)

Average of all observations: Σxᵢ / N.

Mean Absolute Error

Average of absolute errors across measurements.

Standard Deviation (brief)

Statistical measure of spread; square root of variance (not fully discussed, but related to errors).

SI Prefix: kilo- (k)

10³ times the base unit.

SI Prefix: milli- (m)

10⁻³ times the base unit.

SI Prefix: micro- (µ)

10⁻⁶ times the base unit.

SI Prefix: nano- (n)

10⁻⁹ times the base unit.

SI Prefix: mega- (M)

10⁶ times the base unit.

Plane Angle Unit Conversion

1 revolution = 2π rad = 360°.

Conversion Factor (example)

1 m = 100 cm, used via n₁u₁ = n₂u₂.

Density Unit Change

Multiply by (10³ kg / g)(10⁶ cm³ / m³) when converting g/cm³ to kg/m³.

Velocity Unit Change

km h⁻¹ to cm s⁻¹: multiply by (10⁵ cm / km)(1 h / 3600 s).

Dimensional Check of s = ut + ½at²

Both sides have dimension [L]; equation is dimensionally correct.

Dimensional Invalidity Example

v = u + at² is dimensionally inconsistent because at² has dimension [LT⁻¹].

Uses of Significant Figures

Express precision, guide rounding in calculations, compare measurement quality.

Accuracy vs Precision

Accuracy: closeness to true value; Precision: consistency among measurements.

Instrument Calibration

Process of adjusting an instrument to reduce systematic error.

Dimensionless Constant Example

π, e, Avogadro’s number; possess no dimensions or units.

Homogeneity Test (quick)

Compare dimensions term-by-term; inequity => equation wrong.

Time Period of Simple Pendulum (result)

T = 2π √(l/g) (derived via dimensional analysis).

Kinetic Energy Percentage Error

If mass error = 3 %, velocity error = 4 %, then KE error = 3 % + 2×4 % = 11 %.

Parallel Resistance Error Rule

For R₁ ∥ R₂, propagate relative errors through 1/R = 1/R₁ + 1/R₂.

Dimensional Derivation Limitation

Fails when relation involves more than three variable factors.

Physical Correctness

An equation can be dimensionally correct yet not represent true physics (e.g., s = ut + (1/3)at²).