Physics XI - Chapter 02: Units and Measurements
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- Fundamental Quantities: 7 basic quantities: Mass (kg), Length (m), Time (s), Electric Current (A), Temperature (K), Luminous Intensity (cd), Amount of Substance (mol).
- Derived Quantities: Expressed in terms of fundamental quantities (e.g., Force = [M L T⁻²]).
- SI Units: International System of Units; a coherent system based on the seven fundamentals.
- Significant Figures: Meaningful digits in a measurement. Rules: All non-zero digits are significant; Leading zeros are not significant; Captive zeros are significant; Trailing zeros are significant only if after a decimal.
- Rounding Off: If digit to be dropped is more than 5, increase preceding digit by 1; if less than 5, leave it; if exactly 5, make preceding digit even.
- Dimensions: Powers to which fundamental units are raised to represent a physical quantity.
- Dimensional Analysis Uses: To check equation consistency, derive relations, and convert units between systems.
- Principle of Homogeneity: A physical equation is dimensionally correct if each term has the same dimensions.
- Accuracy vs. Precision: Accuracy is closeness to the true value; Precision is the resolution or repeatability of measurements.
- Types of Errors:
- Systematic Errors: Reproducible, consistent error (e.g., instrumental, personal).
- Random Errors: Unpredictable fluctuations (reduced by taking repeated measurements).
- Gross Errors: Mistakes like misreading an instrument.
- Absolute Error: |Measured Value - True Value| (for single measurement) or mean of |aᵢ - ā| for a set.
- Relative Error: Absolute Error / True Value (dimensionless).
- Percentage Error: Relative Error × 100%.
- Error Combination:
- For Z = A ± B: ΔZ = ΔA + ΔB
- For Z = A B or A/B: ΔZ/Z = ΔA/A + ΔB/B
- For Z = Aⁿ: ΔZ/Z = n (ΔA/A)
- Least Count: The smallest value an instrument can measure precisely.
- Vernier Caliper: 1 MSD - 1 VSD
- Screw Gauge: Pitch / Number of Circular Scale Divisions
Basic Level Questions
Chapter Summary
This chapter forms the bedrock of all scientific inquiry. It teaches us that a measurement is meaningless without its unit, establishing the International System of Units (SI) as the global standard for consistency. We learn that every physical quantity can be broken down into its fundamental dimensions of Mass (M), Length (L), and Time (T), among others, allowing us to verify the validity of equations and derive new relationships through Dimensional Analysis.
The concept of Significant Figures instills the discipline of reporting measurements with appropriate precision, reflecting the limitations of our instruments. Crucially, the chapter differentiates between Accuracy and Precision, and classifies errors into systematic, random, and gross, providing the mathematical tools to quantify and propagate uncertainty in calculations.
Finally, we explore precision instruments like the Vernier Caliper and Screw Gauge, which extend our ability to measure beyond the limits of a ordinary scale. In essence, this chapter equips us with the language and tools to quantify the physical world reliably and meaningfully, a skill paramount for any future study in physics or engineering.