Units and Measurement: Class 11 Physics

Introduction to Units and Measurement

• This is the first one-shot session for the 2024-25 series, covering the Units and Measurement chapter.
• Ashu Ghai from Science and Fun is the instructor, focusing on understanding and learning concepts.
• The 11th-grade one-shots from the previous year included experiments, but the Unit and Measurement chapter was divided into multiple parts.
• This year's goal is to cover Units and Measurement in a single one-shot.
• Future one-shots will be presented interestingly, connecting the chapter to real-life examples to enhance enjoyment of physics.

Syllabus Update

• The new NCERT syllabus excludes topics like the parallax method and errors.
• These sections may still be found in older NCERT books.

Quantity

• Anything that can be measured is referred to as quantity.
• Time, mass, and force serve as examples of quantities.
• Emotions like love, hatred, and happiness are not measurable and are not considered quantities.

Units

• Units are symbols or words for measuring quantities.
• Milligrams, grams, and kilograms are units used to measure mass.
• Seconds, minutes, hours, days, weeks, months, and centuries can be used to measure time.
• Units are essential for measuring any quantity.

Types of Units

• Units are divided into fundamental and derived types.
• Physics has seven fundamental units.
• Thousands of other units are derived from these seven fundamental units.
• These seven fundamental units exist for a reason.

Fundamental Units

• These are considered base units and have underlying rationales.
• Examples include:
  • Kilogram (kg) for mass
  • Second (s) for time
  • Ampere (A) for current
  • Meter (m) for length
  • Mole (mol) for amount of substance
  • Candela (cd) for luminous intensity
  • Kelvin (K) for temperature
• Degree Celsius and Fahrenheit are not fundamental units.

Derived Units

• Derived units come from the seven fundamental units.
• Newton (N) is the derived unit for force.
• Force can be expressed as mass × acceleration or kg⋅m/s².
• Pascal (Pa) is the derived unit for pressure.
• Pressure can be expressed as force/area or kg/(m⋅s²).
• Any unit that isn't one of the seven fundamental units is a derived unit.

Dimensions

• Dimensions are symbolic representations of units that remain consistent regardless of the specific unit.
• Time-related quantities can be measured in minutes, seconds, days, hours, or months.
• Units and dimensions are interconnected.
• Dimensions remain constant, although units of the same quantity can differ.
• Mass has a dimension of "M", whether measured in grams, kilograms, etc.
• Time has a dimension of "T", whether measured in minutes, seconds, etc.
• Length has the dimension "L".
• Current has the dimension "A".
• Dimensions are written inside square brackets.

Dimensions of Speed and Velocity

• Speed = Distance / Time
• [Speed] = [Distance] / [Time]
• [Speed] = L / T = LT⁻¹
• The standard representation is: [Speed] = M⁰LT⁻¹

Dimensions of Momentum

• Momentum = Mass × Velocity
• [Momentum] = [Mass] × [Velocity] = M × LT⁻¹ = MLT⁻¹

Dimensions of Kinetic Energy

• Kinetic Energy = 1/2 × m × v²
• [Kinetic Energy] = [Mass] × [Velocity]² = M × (LT⁻¹)² = ML²T⁻²
• All forms of energy share the same dimensions: ML²T⁻²
• Energy and work are equivalent and have the same dimensions and units.

Dimensions of Acceleration

• Acceleration = Change in Velocity / Time
• [Acceleration] = [Velocity] / [Time] = LT⁻¹ / T = LT⁻²

Dimensions of Force

• Force = Mass × Acceleration
• [Force] = [Mass] × [Acceleration] = M × LT⁻² = MLT⁻²

Dimensions of Torque

• Torque = Force × Distance
• [Torque] = [Force] × [Distance] = MLT⁻² × L = ML²T⁻²
• Although torque and energy have the same dimensions, they represent different concepts.

Dimensions of Refractive Index

• Refractive Index = Speed of Light in First Medium / Speed of Light in Second Medium
• [Refractive Index] = [Velocity] / [Velocity] = M⁰L⁰T⁰ (Dimensionless)
• Angles are measured in radians but have no dimensions.

Principle of Homogeneity

• In an equation, each term must have the same units and dimensions.
• Different dimensions cannot be added or subtracted.
• If x + y, then x and y have the same dimensions.
• In an equation with multiple terms, all terms are equal to each other.
• For example, if the equation is x + yt = ab, then x, yt, and ab are all equal.
• Unknown entities can be calculated using this principle if their dimensions are known.

Application of the Principle of Homogeneity - Calculating the Dimension of the Unknown

• Find the dimensions of x in the equation: Speed x Time + x = Area / Length
• (I) All three terms are equal according to the principle of homogeneity.
• (II) Term 1 and term 2 have the same dimensions: [Speed x Time] = [Area / Length]
  • [Speed x Time] = [x]
  • dimension = L
• (III) Another term dimension is also equal:
  • [Area / Length] = [x]
  • [Area / Length] = L² / L
  • = L
• The unknown (x) has a dimension of length.

Application of Principle of Homogeneity - Example 2

• Given the equation: Force x Distance + x = Mass x Acceleration x Height
• (I) All three terms are equal according to the principle of homogeneity.
  • [Force x Distance] = [Mass x Acceleration x Height]
  • = [Force x Distance]
• (II) Insert the dimensions of the term
  • = MLT⁻² x L
  • = ML²T⁻²
• The unknown (x) has the dimension of energy.

Applications of Dimensional Analysis

• Dimensional analysis has three main applications:
  • Checking the dimensional correctness of an equation.
  • Converting units from one system to another.
  • Deriving formulas.

Checking Equations for Dimensional Correctness

• The dimensions of the left-hand side (LHS) of the equation should be equivalent to the right-hand side (RHS).
• For example: LHS: 1/2 m v² = RHS: m g h
• The dimensions of half mL² T⁻² must be the same as m L² T⁻².
• If the LHS has the same dimensions as the RHS, the equation is dimensionally correct.
• Dimensional correctness does not guarantee that the equation is factually correct.

Dimensional Correctness vs. Actual Correctness

• A dimensionally correct equation is not necessarily correct in real life.
• A correct equation in real life will always be dimensionally correct.
• Example: Pressure x Area = Mass x Acceleration
• ML⁻¹ T⁻² x L² = MLT⁻², MLT⁻² = MLT⁻², hence it is dimensionally equal.

Example of Incorrect Dimensional Equation

• Consider Energy / Time = Force / Velocity.
• Dimensionally incorrect: ML²T⁻³ ≠ MT⁻¹.
• An expression is not valid if the LHS and RHS dimensions are not equal.
• If an equation is dimensionally incorrect, then it is an incorrect equation.
• A dimensionally correct equation may or may not be relevant in real-world applications.
• It is unnecessary for some calculations. However, if an equation is dimensionally incorrect, it must be incorrect in reality.

An engaging overview of units and measurement for Class 11 Physics, aligned with the updated NCERT syllabus. Includes real-life examples to enhance understanding. Focuses on measurable quantities and their significance in physics.