Physical Quantities and Units Quiz

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Questions and Answers

What is the maximum percentage error in the measurement of the density of a silver wire with given measurements?

  • 7%
  • 4% (correct)
  • 6%
  • 3%

Taking significant figures into account, what is the result of the operation $9.99 m - 0.0099 m$?

  • 9.980 m
  • 9.98 m
  • 9.9 m (correct)
  • 9.9801 m

What is the correct representation of the mean time period of a second pendulum with a mean absolute error of 0.05s?

  • (2.00 ± 0.10)s
  • (2.00 + 0.025)s
  • (2.00 ± 0.01)s
  • (2.00 ± 0.05)s (correct)

When a thin copper wire increases in length by 2% due to a temperature rise of 10°C, what is the percentage increase in the area of a square copper sheet of the same length?

<p>4% (A)</p> Signup and view all the answers

How is the accuracy of measurement determined?

<p>Percentage Error (C)</p> Signup and view all the answers

What is the correct least count of a vernier caliper when one main scale division is x cm and the n division of the vernier scale coincides with (n – 1) divisions of the main scale?

<p>x/n (D)</p> Signup and view all the answers

For the division of 97.52 by 2.54, which option gives the correct result in terms of significant figures?

<p>38.4 (A)</p> Signup and view all the answers

What is the average absolute error for the period of oscillation values 2.63 s, 2.56 s, 2.42 s, 2.71 s, and 2.80 s?

<p>0.11 s (D)</p> Signup and view all the answers

What is the unit of measurement for solid angle?

<p>Steradian (C)</p> Signup and view all the answers

Which of the following pairs does not have similar dimensions?

<p>Tension and Surface Tension (A)</p> Signup and view all the answers

Which of the following quantities has the same dimensions as energy?

<p>Work (A)</p> Signup and view all the answers

What is the dimension of Planck’s constant equal to?

<p>Angular momentum (C)</p> Signup and view all the answers

What does universal time rely on?

<p>Vibrations of a cesium atom (D)</p> Signup and view all the answers

What is the magnitude of force in another system if it is 100 dyne in CGS units?

<p>3.6 (C)</p> Signup and view all the answers

Which quantity is unitless and always has zero dimensions?

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

Newton-second is the unit of which physical quantity?

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

Flashcards

Magnitude of a physical quantity

The size or extent of a physical quantity, independent of the measurement method.

Unit of solid angle

Steradian (sr). It measures the amount of solid angle around a point.

Unit of momentum

Newton-second (Nâ‹…s).

Unit of energy (not)

Watt (W) is a unit of power, not energy.

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Unit of luminous intensity

Candela (cd).

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Unit of energy (same dimension as)

Torque.

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Dimensionally different pairs (Stress/Tension)

Stress and Surface Tension have different dimensions.

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Quantities with same dimensions as Energy

Work and Power (although power is energy per unit time)

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Dimensional Analysis

A technique used to check the consistency of equations by examining the dimensions of physical quantities involved. It ensures that both sides of an equation have the same units.

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Significant Figures

The meaningful digits in a measurement, including all certain digits and the first uncertain digit. They indicate the precision of the measurement.

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Percentage Error

The ratio of the absolute error to the true or accepted value, expressed as a percentage. It quantifies the relative uncertainty in a measurement.

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Least Count

The smallest value that can be measured by an instrument. It determines the precision of the instrument.

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Vernier Caliper

A precise measuring instrument used to measure small distances with higher accuracy than rulers. It utilizes a vernier scale that slides against a main scale.

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Absolute Error

The difference between the measured value and the true or accepted value. It represents the uncertainty in a single measurement.

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Average Absolute Error

The average of all absolute errors in a set of measurements. It provides an overall estimate of the uncertainty in a series of readings.

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Accuracy vs. Precision

Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other.

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Study Notes

Physical Quantities and Units

  • Magnitude of physical quantity: Independent of measurement method. Directly proportional to fundamental units (mass, length, time).
  • Solid angle unit: Steradian.
  • Newton-second unit: Momentum.
  • Energy units: Calorie, Joule, Electron Volt. Watt is a unit of power, not energy.
  • Candela unit: Luminous intensity.
  • Universal time basis: Vibrations of a cesium atom.
  • Energy-equivalent dimensions: Torque.
  • Quantities with different dimensions: Tension and surface tension.
  • Quantities with same dimensions: Work and energy, momentum and impulse.
  • Unitless quantity: Never has a non-zero dimension.
  • Dimensions of Planck's constant/moment of inertia ratio: Frequency.
  • Dimensions of Planck's constant equivalent: Angular momentum.
  • Quantities with different dimensions: Momentum and Planck's constant.
  • Force magnitude conversion (CGS to other system): 3.6.
  • Energy unit conversion (new system): 1/16.
  • Dimensional analysis limitations: Cannot determine exact relationships between physical quantities. Cannot distinguish quantities with identical dimensions.
  • Significant figures example: 9.99m - 0.0099m = 9.98m; 97.52/2.54 = 38.4.
  • Maximum percentage error example: Density calculation → 4%

Measurement Errors and Significant Figures

  • Significant figures rule: Results should reflect the precision of the least precise measurement.
  • Mean absolute error example: 0.11s
  • Accuracy determination: Percentage error.
  • Percentage error in volume calculation example: 3%.
  • Calculating the least count of vernier calipers: x/(n−1)

Other Concepts

  • Linear expansion: 2% increase in length for 10°C
  • Area expansion: 4% increase.
  • Vernier calipers least count: x/n (where x is main scale division and n is the number of vernier divisions)

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