1. Introduction

This chapter covers the fundamentals of measurement in physics: physical quantities, SI units, dimensional analysis, significant figures, errors, and key formulas — essential for JEE Mains, JEE Advanced, NEET & CBSE.

2. Physical Quantities & Units

• Fundamental Quantities: Length, Mass, Time, Electric Current, Temperature, Amount of Substance, Luminous Intensity
• Derived Quantities: Speed, Force, Pressure, etc.
• SI Units: Standard global units—learn more on Wikipedia

3. Systems of Units

Supplementary units: radian and steradian for angles.

4. Measurement Techniques

Length

Use vernier calipers and screw gauge for precision. Also utilize meter scale and parallax method for large-scale measurements.

Mass

Measured using beam or electronic balances.

Time

Measured via stopwatch, clocks, or atomic clocks (~10⁻¹³ s precision).

5. Significant Figures & Precision

Significant figures reflect measurement accuracy, while precision indicates consistency of repeated readings.

• All non-zero digits are counted
• Zeros between non-zero digits are significant
• Trailing zeros in decimal form are significant

Examples: 0.00456 → 3 sig‑figs; 500.0 → 4 sig‑figs.

6. Errors & Uncertainty

Types of Errors:

• Systematic: calibration or instrument bias
• Random: unpredictable variations
• Gross: human mistakes

Error Calculations:

• Absolute error: ΔA = |measured − true value|
• Relative error: ΔA ÷ true value
• Percentage error: (ΔA ÷ true value) × 100%

Propagation: add absolute errors in sums/differences, and relative errors in multiplication/division.

7. Dimensional Analysis

Dimensional formula expresses physical dimensions as [MaLbTc]. Example: Force = mass × acceleration → [M¹L¹T⁻²].

• Check equation validity
• Derive and confirm formulae
• Perform unit conversions

8. Formulae Summary

9. Watch: Units & Measurement Explained

10. FAQs

Q: Why are SI units important?
A: They standardize measurements globally for accuracy and consistency.

Q: What is the principle of homogeneity?
A: Equations are valid only if both sides have identical dimensions.

Q: How do you combine errors in multiplication?
A: Add the relative errors of each factor to get the final error.

Q: What is dimensional analysis and why is it important?
A: It’s a method used to check the validity of equations and convert units by analyzing the dimensions of physical quantities.

Q: How is the accuracy of Vernier Calipers and Screw Gauge different?
A: Vernier Calipers offer ~0.1 mm precision, while Screw Gauges provide higher precision (~0.01 mm), ideal for small object measurements.