Fundamental and Derived Quantities in Physics

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Questions and Answers

Which of the following is a derived quantity?

  • Time
  • Length
  • Mass
  • Velocity (correct)

What does the principle of homogeneity state?

  • Physical quantities with the same dimensions can be added or subtracted.
  • Physical quantities with different dimensions can be multiplied.
  • Physical quantities with the same dimensions can be divided.
  • All of the above (correct)

What is the unit of force in the FPS system?

Pound

What is the formula for the maximum fractional error in the product of two quantities?

<p>$\frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B}$</p> Signup and view all the answers

Dimensional analysis can predict the numerical value of a physical quantity.

<p>False (B)</p> Signup and view all the answers

What is the least count of a Vernier caliper?

<p>1 MSD - 1 VSD</p> Signup and view all the answers

What is the formula for calculating the total reading of a screw gauge?

<p>Total Reading = L.S.R + C.S.R</p> Signup and view all the answers

What is the purpose of rounding off numbers?

<p>To simplify numbers and maintain the same level of precision in calculations.</p> Signup and view all the answers

Which of the following is NOT a significant figure rule?

<p>Leading zeros are significant. (B)</p> Signup and view all the answers

Match the following physical quantities with their dimensions:

<p>Length = L Time = T Mass = M Velocity = LT⁻¹ Force = MLT⁻² Energy = ML²T⁻²</p> Signup and view all the answers

Flashcards

Fundamental Quantities

Physical quantities that are independent of other quantities for their measurement.

Derived Quantities

Quantities that can be expressed based on fundamental quantities.

Significant Figures

The number of digits that contribute to the precision of a measurement, including all non-zero digits and significant zeros.

Addition and Subtraction with Significant Figures

The number of decimal places in the result of addition or subtraction is determined by the term with the fewest decimal places.

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Multiplication and Division with Significant Figures

The number of significant figures in the result of multiplication or division matches the factor with the fewest significant figures.

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Principle of Homogeneity

Ensures that the dimensions of each term in an equation are consistent.

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Dimensions of a Physical Quantity

The expression of a physical quantity in terms of fundamental quantities, represented as powers.

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Dimensional Analysis

A technique for checking the correctness of a formula, establishing relationships between quantities, and converting units.

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Vernier Calliper

The instrument with a movable jaw that slides along a main scale and a vernier scale, used for precise length measurements.

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Least Count of a Vernier Calliper

The smallest length that can be measured with a Vernier Calliper, determined by the difference between one main scale division and one vernier scale division.

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Screw Gauge

An instrument using a micrometer screw with a linear scale and a circular scale, for measuring very small lengths.

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Pitch of a Screw Gauge

The distance the screw gauge moves per full rotation of the circular scale.

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Least Count of a Screw Gauge

The smallest distance that can be measured with a screw gauge, determined by the pitch and the number of divisions on the circular scale.

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Error in Measurement

The difference between the measured value and the true value of a quantity.

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Mean Absolute Error

The average of the absolute values of individual errors.

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Relative Error or Fractional Error

The ratio of the mean absolute error to the mean value of the measurement, expressed as a fraction.

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Percentage Error

The relative error expressed as a percentage, indicating the error proportion.

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Combination of Errors

The combination of errors occurring in different measurements.

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Representation of Errors

A numerical representation of the final result of a measurement, showing the measured value and its associated error.

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Mean Value of Measurement

The value obtained by repeating a measurement multiple times and averaging the results.

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Rounding Off

The process of adjusting a numerical value to a specific number of significant figures.

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FPS System

A system where length is measured in feet, mass in pounds, and time in seconds.

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CGS System

A system for measuring length in centimeters, mass in grams, and time in seconds.

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MKS System

A system where length is measured in meters, mass in kilograms, and time in seconds.

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Checking Correctness of a Formula

A technique used to check the correctness of a formula by examining the dimensions of each term.

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Establishing Relationships

A method for establishing relationships between quantities based on their dimensions.

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Converting Values

A technique for converting the value of a quantity from one system of units to another.

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Limitations of Dimensional Analysis

Limitations of Dimensional Analysis

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Not Predicting Numerical Values

It can't predict the numerical value or constant in a relation.

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Not Working with Certain Functions

It doesn't work with trigonometric, logarithmic, or exponential functions.

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Not Providing Information About Constants

It doesn't provide information about constants or the nature (vector/scalar) of a quantity.

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Study Notes

Fundamental Quantities

  • Physical quantities independent of others for measurement
  • Examples: mass, length, time, temperature, electric current, luminous intensity, and amount of substance

Derived Quantities

  • Quantities expressed in terms of fundamental quantities
  • Examples: angle, speed, velocity, acceleration, force

Systems of Units

  • FPS (Foot-Pound-Second): Length in feet, mass in pounds, time in seconds
  • CGS (Centimeter-Gram-Second): Length in centimeters, mass in grams, time in seconds
  • MKS (Meter-Kilogram-Second): Length in meters, mass in kilograms, time in seconds

Principle of Homogeneity

  • Physical quantities with same dimensions can be added/subtracted
  • Dimensions of both sides of an equation must be equal

Dimensional Analysis

  • Fundamental/base quantities and their powers to express a physical quantity
  • Example: Force [F] = [MLT-2]

Usage of Dimensional Analysis

  • Checking correctness of formulas
  • Establishing relations between quantities
  • Converting units between systems

Limitations of Dimensional Analysis

  • Cannot predict numerical values
  • Does not derive trigonometric, logarithmic, or exponential relationships
  • Does not indicate if a quantity is vector or scalar

Significant Figures (Significant Digits)

  • Rules for determining significant figures:
    • All non-zero digits are significant
    • Zeros between non-zero digits are significant
    • Leading zeros are not significant
    • Trailing zeros in a decimal are significant
    • Trailing zeros in a whole number are not significant (unless known from measurement)
    • Exponential form does not affect significant figures

Rules for Arithmetic Operations with Significant Figures

  • Addition/subtraction: Result has same number of decimal places as the term with fewest decimal places
  • Multiplication/division: Result has same number of significant figures as the factor with fewest significant figures

Rounding Off

  • If digit to be rounded is 5 or greater, preceding digit increases by 1
  • If digit to be rounded is less than 5, preceding digit remains unchanged
  • If digit to be rounded is 5, preceding digit increases by 1 if odd, remains same if even

Representation of Errors

  • Mean absolute error: Sum of absolute errors divided by the total number of measurements
  • Final result of measurement can be written as: α = α1 ± Δα

Relative/Fractional Error

  • Ratio of mean absolute error to mean value of measurement

Percentage Error

  • Relative error multiplied by 100%

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