NCERT Class 11 Physics Chapter 1 Formula Sheet: Units and Measurements
Welcome to our comprehensive formula sheet for NCERT Class 11 Physics Chapter 1, "Physical World and Measurement." This chapter lays the foundation for understanding units, dimensional analysis, errors in measurement, and significant figures. Whether you're preparing for exams or revising key concepts, this formula sheet is designed to help you grasp the essentials quickly and effectively.
📏 Units and Measurements
Fundamental and Derived Units
SI Unit of Length: Meter (m) - The standard unit for measuring length or distance.
SI Unit of Mass: Kilogram (kg) - The standard unit for measuring mass.
SI Unit of Time: Second (s) - The standard unit for measuring time.
SI Unit of Force: Newton (N) = [M L T⁻²] - Derived unit for force, equivalent to kg·m/s².
SI Unit of Work/Energy: Joule (J) = [M L² T⁻²] - Derived unit for energy or work, equivalent to N·m.
📐 Dimensional Analysis
Key Formulas and Examples
Dimensional Formula: [Mᵃ Lᵇ Tᶜ] - Represents the powers of fundamental units (Mass, Length, Time).
Examples:
Velocity = [M⁰ L¹ T⁻¹] - Dimension of speed, i.e., distance/time.
Acceleration = [M⁰ L¹ T⁻²] - Dimension of velocity/time.
Force = [M¹ L¹ T⁻²] - Dimension of mass × acceleration.
Principle of Homogeneity: Dimensions on both sides of a physical equation must be equal - Ensures the equation is dimensionally consistent.
⚖️ Errors in Measurement
Error Calculations
Absolute Error: Δa = |a_measured - a_true| - Difference between measured and actual value.
Mean Absolute Error: Δa_mean = Σ|Δa_i| / n - Average of absolute errors over n measurements.
Relative Error: δa = Δa_mean / a_mean - Ratio of mean absolute error to mean value.
Percentage Error: δa × 100% - Relative error expressed as a percentage.
Combination of Errors
For sum/difference (Z = A ± B): ΔZ = ΔA + ΔB - Error in sum or difference is the sum of individual errors.
For product/quotient (Z = A × B or A / B): ΔZ/Z = ΔA/A + ΔB/B - Relative error in product or quotient is the sum of relative errors.
For power (Z = Aⁿ): ΔZ/Z = n × ΔA/A - Relative error in a power is n times the relative error of the base.
🔢 Significant Figures
Rules and Operations
Rules for Significant Figures:
1. All non-zero digits are significant - E.g., 123 has 3 significant figures.
2. Zeros between non-zero digits are significant - E.g., 1002 has 4 significant figures.
3. Leading zeros are not significant - E.g., 0.0023 has 2 significant figures.
4. Trailing zeros in a decimal number are significant - E.g., 12.00 has 4 significant figures.
Addition/Subtraction: Result has same decimal places as the least precise number - E.g., 12.3 + 4.567 = 16.9 (one decimal place).
Multiplication/Division: Result has same significant figures as the number with fewest significant figures - E.g., 2.3 × 4.567 = 11 (2 significant figures).
This NCERT Class 11 Physics Chapter 1 formula sheet is a concise resource for students aiming to master the fundamentals of units, measurements, dimensional analysis, errors, and significant figures. Use it as a quick reference for revision or exam preparation, and explore our website for more Physics resources!
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Note: This formula sheet is based on NCERT Class 11 Physics Chapter 1. For detailed explanations and examples, refer to the NCERT textbook.
