Class 11 · Chapter 2
Physical World & Measurement
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
Physical World & Measurement Short Notes
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Condensed revision points for Physical World & Measurement — for quick recall before exams, not a substitute for the full notes.
Quantities, Units & Systems
- Q = n × u; larger unit ⇒ smaller numerical value (n₁u₁ = n₂u₂).
- Fundamental quantities (7): mass, length, time, temperature, current, luminous intensity, amount of substance.
- Supplementary units: radian (plane angle), steradian (solid angle) — both dimensionless.
- SI prefixes: kilo 10³, mega 10⁶, giga 10⁹ | milli 10⁻³, micro 10⁻⁶, nano 10⁻⁹, pico 10⁻¹².
- km/hr → m/s: multiply by 5/18.
Dimensional Formulas to Memorise
- Velocity [LT⁻¹], Acceleration [LT⁻²]
- Force [MLT⁻²], Work/Energy/Torque [ML²T⁻²]
- Power [ML²T⁻³], Pressure/Stress [ML⁻¹T⁻²]
- Momentum [MLT⁻¹], Gravitational constant G [M⁻¹L³T⁻²]
- Angle, strain, refractive index — all dimensionless [M⁰L⁰T⁰].
Uses & Limits of Dimensional Analysis
- Can: find units, check homogeneity of an equation, convert between systems, guess a relation among known dependent quantities.
- Cannot: find dimensionless constants (2π, ½...), handle trig/exponential/log relations, work with >3 dependent quantities, or distinguish quantities with the same dimensional formula (e.g. work vs torque).
Significant Figures — Quick Rules
- All non-zero digits significant; zero between two non-zero digits significant.
- Leading zeros never significant; trailing zeros after a decimal point ARE significant.
- Scientific notation: only the decimal part's digits count, not the power of 10.
- Multiply/divide → match the fewest sig figs; add/subtract → match the fewest decimal places.
Errors — Definitions
- Mean value aₘ = Σaᵢ/n (best estimate of true value).
- Absolute error Δaᵢ = aₘ − aᵢ; Mean absolute error = Σ|Δaᵢ|/n.
- Relative error = Δa(mean)/aₘ; Percentage error = relative error × 100%.
Error Propagation — Memorise This Table
- Sum/Difference (x = a ± b): absolute errors ADD → Δx = Δa + Δb.
- Product/Quotient (x = ab or a/b): relative errors ADD → Δx/x = Δa/a + Δb/b.
- Power (x = aᵏ): relative error scales by k → Δx/x = k(Δa/a).
- Errors never cancel — even subtraction adds the absolute errors.
- Measure the quantity with the highest power most carefully — its error gets amplified most.
Vernier Caliper
- Least count (VC) = 1 MSD − 1 VSD = (1/n) MSD, for n VSD = (n−1) MSD.
- Ordinary caliper: VC = 0.1 mm = 0.01 cm.
- Reading = MSR + (VSR × VC).
- Positive zero error → subtract correction; negative zero error → add correction.
Screw Gauge
- LC = Pitch / (number of circular scale divisions).
- Typical: pitch 1 mm, 100 divisions → LC = 0.01 mm.
- Reading = Linear scale reading + (Circular scale reading × LC).
- Zero error correction applied the same way as in vernier calipers.
Common Exam Traps
- Don't confuse precision (number of digits/least count) with accuracy (closeness to true value).
- Dimensionally correct ≠ numerically correct — constants like 2π can't be checked this way.
- Subtraction of two close, large quantities can drastically increase percentage error even if absolute error looks small.
- Always state the final answer with the correct number of significant figures, not just whatever the calculator displays.
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