Measurement (Unit 01) - Study Guide
Syllabus core resource book summary and exam-standard virtual practical simulator.
Syllabus Core Concepts
- • 7 Base Quantities: Length (m), Mass (kg), Time (s), Temperature (K), Electric Current (A), Amount of Substance (mol), Luminous Intensity (cd).
- • Percentage Error: As the measured value increases, the percentage error decreases. (Measuring 10 m with a meter rule is more precise than measuring 10 cm).
- • Spherometer Formula: Radius of curvature R = a² / 6h + h / 2.
Marking Secrets & Traps
📘 Resource Book Summary: Measurement
Core Definitions:
- • Base Quantities: Independent physical quantities that cannot be defined in terms of other quantities.
- • Derived Quantities: Quantities derived by multiplying or dividing two or more base quantities.
Key Points:
- • There are 7 base quantities and 2 supplementary quantities (plane angle and solid angle) in SI.
- • Never use plural forms in unit symbols (e.g. 5 kg, not 5 kgs).
⚠️ Exam Trap Notes:
When writing compound units as products, a single space is mandatory between base unit symbols (e.g., 10 m s⁻¹ is correct; 10 ms⁻¹ means per millisecond, not meters per second).
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Electric Current | ampere | A |
| Amount of Substance | mole | mol |
| Luminous Intensity | candela | cd |
Definitions:
Dimensions: Symbolic representation showing how a physical quantity is related to base quantities.
Equations:
Dimensional Homogeneity: If a = bc + d/e, then [a] = [bc] = [d/e] must be satisfied.
⚠️ Exam Traps:
You cannot determine dimensionless constants in equations using dimensional analysis alone.
Definitions:
- • Systematic Errors: Errors in one direction caused by instrument faults or misuse.
- • Random Errors: Unpredictable errors during measurements. Mitigated by averaging.
- • Least Count: The smallest division an instrument can measure.
Formula:
Percentage Error = (Absolute Error / Measured Value) × 100%
⚠️ Exam Traps:
A meter rule has a least count of 1 mm. To keep percentage error below 1%, the minimum length measured must be at least 100 mm (10 cm).
📐 Micrometer Screw Gauge Virtual Lab
Device has a constant Zero Error = -0.02 mm.