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Questions and Answers
Which of the following is a derived quantity?
Which of the following is a derived quantity?
What does the principle of homogeneity state?
What does the principle of homogeneity state?
What is the unit of force in the FPS system?
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?
What is the formula for the maximum fractional error in the product of two quantities?
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Dimensional analysis can predict the numerical value of a physical quantity.
Dimensional analysis can predict the numerical value of a physical quantity.
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What is the least count of a Vernier caliper?
What is the least count of a Vernier caliper?
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What is the formula for calculating the total reading of a screw gauge?
What is the formula for calculating the total reading of a screw gauge?
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What is the purpose of rounding off numbers?
What is the purpose of rounding off numbers?
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Which of the following is NOT a significant figure rule?
Which of the following is NOT a significant figure rule?
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Match the following physical quantities with their dimensions:
Match the following physical quantities with their dimensions:
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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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Description
Explore the differences between fundamental and derived physical quantities in this quiz. Learn about various systems of units, the principle of homogeneity, and the importance of dimensional analysis. Test your understanding of these essential concepts in physics.
