Units and Measurements in One Shot | NCERT Class 11 Physics Chapter-2 Dimensional Analysis Revision

Units and Measurement - Detailed Transcript

Key Concepts:

• Physical Quantity
• Fundamental Quantity
• Derived Quantity
• Supplementary Quantity
• Scalar Quantity
• Vector Quantity
• Units (SI, CGS, MKS, FPS)
• Dimensions
• Accuracy
• Precision
• Error
• Significant Figures
• Rounding Off
• Plane Angle
• Solid Angle

1. Introduction and Chapter Overview:

• The chapter "Units and Measurement" is divided into two main parts:
  • Physical Quantities: Includes the study of units, dimensions, dimensional analysis, applications, and limitations.
  • Measurement: Covers measurement processes, errors in measurement, significant figures, and rounding off rules.
• The chapter also covers accuracy and precision.

2. Defining Physical Quantities:

• A physical quantity is something that can be measured using an instrument, either directly or indirectly.
• It is also used to define or apply laws of physics.
• Example: Time, weight, and volume are physical quantities, while motivation is not because it cannot be directly measured by an instrument.
• Definition: A physical quantity is used to describe the laws of physics and can be measured directly or indirectly by an instrument.

3. Classification of Physical Quantities:

• Based on Dependency:
  • Fundamental Quantities: Independent and basic quantities used to derive other quantities.
  • Derived Quantities: Quantities derived using fundamental quantities.
  • Supplementary Quantities: Additional quantities (plane angle and solid angle).
• Based on Directional Properties:
  • Scalar Quantities: Quantities with magnitude only.
  • Vector Quantities: Quantities with both magnitude and direction.

4. Fundamental Physical Quantities:

• There are seven fundamental physical quantities:
  • Mass (M)
  • Length (L)
  • Time (T)
  • Temperature (T or θ or K)
  • Electric Current (I or A)
  • Amount of Substance (mol)
  • Luminous Intensity (cd)
• Each quantity has a specific symbol for representation.

5. Derived Physical Quantities:

• Derived quantities are derived from fundamental quantities.
• Example:
  • Velocity = Displacement / Time (L/T)
  • Acceleration = Change in Velocity / Time (L/T²)
  • Force = Mass × Acceleration (M × L/T²)

6. Units of Measurement:

• A unit is a standard quantity used for measurement.
• Procedure for Selecting a Unit:
  • Accurately defined.
  • Suitable size.
  • Should not change with time and conditions.
  • Easy to access and reproduce.

7. Systems of Units:

• CGS System: Centimeter, Gram, Second.
• MKS System: Meter, Kilogram, Second.
• FPS System: Foot, Pound, Second.
• SI System (International System of Units):
  • Length: Meter (m)
  • Mass: Kilogram (kg)
  • Time: Second (s)
  • Electric Current: Ampere (A)
  • Temperature: Kelvin (K)
  • Amount of Substance: Mole (mol)
  • Luminous Intensity: Candela (cd)

8. Supplementary Physical Quantities:

• Plane Angle (θ):
  • Defined in 2D.
  • θ = Arc / Radius
  • Unit: Radian (rad)
  • Full Revolution: 2π radians
  • Half Revolution: π radians
• Solid Angle (Ω):
  • Defined in 3D.
  • Ω = Area / Radius²
  • Unit: Steradian (sr)

9. Dimensions:

• Dimensions indicate how many times a fundamental quantity is used in a physical quantity.
• Definition: The powers to which the fundamental quantities must be raised to represent a given physical quantity.
• Symbols:
  • Length: [L]
  • Mass: [M]
  • Time: [T]
  • Current: [A] or [I]
  • Temperature: [K] or [θ]
  • Amount of Substance: [mol]
  • Luminous Intensity: [cd]
• Example:
  • Area: [L²]
  • Volume: [L³]
  • Acceleration: [M⁰L¹T⁻²]
  • Force: [M¹L¹T⁻²]

10. Steps to Determine Dimensional Formula:

1. Know the formula of the physical quantity in terms of fundamental quantities.
2. Represent each fundamental quantity with its symbol.
3. Simplify the expression to obtain the dimensional formula.

11. Units of Force:

• SI Unit: Kilogram meter per second squared (kg⋅m/s²) or Newton (N)
• CGS Unit: Gram centimeter per second squared (g⋅cm/s²) or Dyne

12. Conclusion:

• The chapter covers the basics of units and measurement, including the definition and classification of physical quantities, different systems of units, and the concept of dimensions.
• Understanding these concepts is essential for solving problems in physics.