Physical Quantities and Units Quiz

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

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

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

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?

How is the accuracy of measurement determined?

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?

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

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?

What is the unit of measurement for solid angle?

Which of the following pairs does not have similar dimensions?

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

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

What does universal time rely on?

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

Which quantity is unitless and always has zero dimensions?

Newton-second is the unit of which physical quantity?

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)

Test your understanding of physical quantities and their units with this quiz. Topics include dimensional analysis, energy units, and conversion factors. Perfect for students learning about fundamental concepts in physics.