Free NEET Mock Tests for Units And Measurements

• Syllabus: ⬥ Physics: Scope and excitement; nature of physical laws; Physics, technology and society.
  ⬥ Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures.
  ⬥ Dimensions of physical quantities, dimensional analysis and its applications.

A brief overview on Physicsl World and Measurement

• "Physical World and Measurement" is a fundamental concept in physics because it lays the groundwork for understanding the natural phenomena and processes that occur in our physical world. Lets go through a brief overview on Physical World and Measurement.
• What is physical quantity? A physical quantity is a measurable property or characteristic of an object or phenomenon that can be quantitatively described using numbers and units. In physics, physical quantities can be classified into two main types:
• Scalar Quantities: Scalar quantities have magnitude (numerical value) only and no direction. Examples of scalar quantities include mass, volume, temperature, and speed.
• Vector Quantities: Vector quantities have both magnitude and direction. They are represented by arrows in physics, where the length of the arrow represents the magnitude, and the direction of the arrow indicates the direction of the quantity. Examples of vector quantities include displacement, velocity, acceleration, force, and momentum.
• Importance of Measurements of Physical quantities: Physical quantities are essential in physics because they allow scientists and engineers to describe and analyze various phenomena, formulate mathematical relationships, conduct experiments, and make predictions. The measurement of physical quantities involves defining appropriate units (such as meters, kilograms, seconds, etc.) to quantify the magnitude of the quantity being measured.
• Definition of units of measurement: Units of measurement are standardized quantities used to express the magnitude of physical quantities. In simple terms, they are specific values or standards used to measure and quantify different aspects of the physical world. These units provide a common language for scientists, engineers, and researchers to communicate numerical data accurately and precisely.
• Physical Quantities and Units:

Physical Quantity	CGS Units	FPS Units	MKS Units	Relation between Units
Length	Centimeter (cm)	Foot (ft)	Meter (m)	1 m = 100 cm = 3.25 ft
Mass	Gram (g)	Pound (lb)	Kilogram (kg)	1 kg = 1000 g = 2.20462 lb
Time	Second (s)	Second (s)	Second (s)	1 s = 1 s = 1 s
Area	Square Centimeter (cm2)	Square Foot (ft2)	Square Meter (m2)	1 m2 = 10000 cm2 = 10.7639 ft2
Volume	Cubic Centimeter (cm3)	Cubic Foot (ft3)	Cubic Meter (m3)	1 m3 = 1000000 cm3 = 35.3147 ft3
Density	Gram per Cubic Centimeter (g/cm3)	---	Kilogram per Cubic Meter (kg/m3)	1 kg/m3 = 1000 g/cm3
Velocity	Centimeter per Second (cm/s)	Foot per Second (ft/s)	Meter per Second (m/s)	1 m/s = 100 cm/s = 3.28084 ft/s
Acceleration	Centimeter per Second Squared (cm/s2)	Foot per Second Squared (ft/s2)	Meter per Second Squared (m/s2)	1 m/s2 = 100 cm/s2 = 3.28084 ft/s2
Force	Dyne (dyn)	Pound Force (lbf)	Newton (N)	1 N = 10^5 dyn = 0.224809 lbf
Pressure	Dyne per Square Centimeter (dyn/cm2)	Pound Force per Square Inch (psi)	Pascal (Pa)	1 Pa = 10 dyne/cm2 = 0.000145037 psi
Work or Energy	Erg (erg)	Foot-Pound (ft-lbf)	Joule (J)	1 J = 10^7 erg = 0.737562 ft-lbf
Power	Erg per Second (erg/s)	Foot-Pound per Second (ft-lbf/s)	Watt (W)	1 W = 10^7 erg/s = 0.737562 ft-lbf/s

• Different types of unit systems: There are several types of unit systems used in science and engineering to measure physical quantities. Some of the most common unit systems include:
  1. ⬥ 1. International System of Units (SI): SI is the modern form of the metric system and is widely used in scientific and technical fields worldwide. It is based on seven fundamental units: meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity). SI units are coherent, meaning they are interconnected through mathematical relationships and conversions.
  2. ⬥ 2. Centimeter-Gram-Second (CGS) System: The CGS system is an older metric system that uses centimeters for length, grams for mass, and seconds for time. It is commonly used in certain fields like electromagnetism and optics due to historical reasons and convenience in certain calculations.
  3. ⬥ 3. Foot-Pound-Second (FPS) System: The FPS system, also known as the British Engineering System (BES), uses feet for length, pounds for mass, and seconds for time. It was historically used in the United Kingdom and the United States but has largely been replaced by the SI system in scientific and engineering contexts.
  4. ⬥ 4. International System of Units (MKS): The MKS system is a variant of the metric system that uses meters for length, kilograms for mass, and seconds for time. It is similar to the SI system but predates the adoption of the SI units.
• The dimensions of physical quantities: The dimensions of physical quantities are expressed using a system of dimensional analysis, where different physical quantities are represented by fundamental dimensions. These fundamental dimensions are typically denoted by letters such as M, L, T, etc., representing mass, length, time, and other relevant dimensions.
• Table of physical quantities with their dimensions and Units:

Physical Quantity	Dimension	SI Unit
Length	L	Meter (m)
Angle	Θ	Radian (rad)
Solid Angle	Ω	Steradian (sr)
Area	L²	Square Meter (m²)
Volume	L³	Cubic Meter (m³)
Density	ML⁻³	Kilogram per Cubic Meter (kg/m³)
Velocity	LT⁻¹	Meter per Second (m/s)
Acceleration	LT⁻²	Meter per Second Squared (m/s²)
Force	MLT⁻²	Newton (N)
Pressure	ML⁻¹T⁻²	Pascal (Pa)
Work or Energy	ML²T⁻²	Joule (J)
Power	ML²T⁻³	Watt (W)
Surface Tension	MT⁻²	Newton per Meter (N/m)
Viscosity	ML⁻¹T⁻¹	Pascal Second (Pa·s)
Heat Capacity	ML²T⁻²Θ⁻¹	Joule per Kelvin (J/K)
Frequency	T⁻¹	Hertz (Hz)
Current	I	Ampere (A)
Charge	QT⁻¹	Coulomb (C)
Specific Heat	ML⁻¹T⁻²Θ⁻¹	Joule per Kilogram Kelvin (J/(kg·K))
Latent Heat	ML²T⁻²	Joule (J)
Molar Specific Heat	LT⁻²Θ⁻¹	Joule per Mole Kelvin (J/(mol·K))
Heat Conductivity	MLT⁻³Θ⁻¹	Watt per Meter Kelvin (W/(m·K))
Molar Gas Constant	ML²T⁻²Θ⁻¹N⁻¹	Joule per Mole Kelvin (J/(mol·K))
Electric Potential	ML²T⁻³I⁻¹	Volt (V)
Electric Field	MT⁻²I⁻¹	Newton per Coulomb (N/C)
Resistance	ML²T⁻³I⁻²	Ohm (Ω)

• Instruments of Measurements: Instruments of Measurements" refers to devices or tools used to quantify physical quantities accurately. These instruments are designed to measure various properties such as length, mass, time, temperature, electric current, and more. They play a crucial role in scientific experiments, industrial processes, and everyday activities where precise measurements are essential. Common instruments of measurements include rulers, vernier calipers, micrometers, thermometers, balances, voltmeters, ammeters, and oscilloscopes, among others. Each instrument is specialized for specific types of measurements and operates based on fundamental principles of physics, such as the expansion of materials with temperature changes or the flow of electricity in circuits.
• List of Instruments of Measurements:

Physical Quantity	Instruments of Measurements
Length	Ruler, Vernier Calipers, Micrometer, Laser Distance Meter
Angle	Protractor, Theodolite, Sextant
Solid Angle	Sphere Calorimeter
Area	Area Meter, Planimeter
Volume	Volumetric Flask, Graduated Cylinder
Density	Density Balance, Hydrometer
Velocity	Speedometer, Doppler Radar
Acceleration	Accelerometer
Force	Spring Balance, Force Gauge
Pressure	Barometer, Manometer, Pressure Gauge
Work or Energy	Spring Scale, Energy Meter
Power	Wattmeter, Power Analyzer
Surface Tension	Surface Tensiometer
Viscosity	Viscometer, Rotational Viscometer
Heat Capacity	Calorimeter, Heat Capacity Meter
Frequency	Frequency Counter, Oscilloscope
Current	Ammeter, Multimeter
Charge	Coulombmeter, Electrometer
Specific Heat	Specific Heat Capacity Apparatus
Latent Heat	Latent Heat Apparatus
Molar Specific Heat	Molar Specific Heat Apparatus
Heat Conductivity	Thermal Conductivity Apparatus
Molar Gas Constant	Gas Constant Apparatus
Electric Potential	Voltaic Cell, Potentiometer
Electric Field	Electrostatic Field Meter
Resistance	Ohmmeter, Multimeter

• Significant figures: Significant figures, also known as significant digits, are digits in a numerical value that contribute to its accuracy and precision. These figures indicate the reliability of a measurement or calculation and help convey the certainty of the measured quantity. Here are the key points about significant figures:
• ⬥ Definition: Significant figures are the digits in a number that are known with certainty plus the first uncertain digit. They represent the meaningful and reliable digits in a numerical value.
• ⬥ Purpose: Significant figures are used to communicate the precision of a measurement or calculation. They help convey the level of confidence in the reported value.
• ⬥ Rules for Determining Significant Figures:

  * All non-zero digits are significant. For example, in the number 456, all three digits (4, 5, and 6) are significant.
  * Zeroes between non-zero digits are significant. For example, in the number 405, all three digits (4, 0, and 5) are significant.
  * Leading zeroes (zeros to the left of non-zero digits) are not significant. For example, in the number 0.0032, the significant figures are 3 and 2.
  * Trailing zeroes (zeros to the right of non-zero digits after a decimal point) are significant. For example, in the number 32.00, all four digits (3, 2, 0, and 0) are significant.

• Accuracy and precision: Accuracy and precision are two important concepts in the context of measurements and data analysis. Here is a brief discussion on accuracy and precision:
• ⬥ Accuracy: Accuracy refers to how close a measured or calculated value is to the true or accepted value. It indicates the degree of correctness or correctness of a measurement or calculation. A measurement is considered accurate if it is very close to the true value, with minimal errors or deviations. Accuracy is often expressed as a percentage error or deviation from the accepted value.
• ⬥ Precision: Precision refers to the level of repeatability, consistency, or reproducibility of measurements or data points. It indicates how closely individual measurements or data points agree with each other. A measurement or data set is considered precise if the values are tightly clustered or have low variability around a central value. Precision is often expressed in terms of standard deviation, variance, or the spread of data points around the mean.
• Comparison between Accuracy & Precision:

  	Accuracy	Precision
  Definition	The degree of closeness of a measured value to the true value.	The degree of consistency or repeatability of measurements.
  Goal	To obtain results that are close to the actual or accepted value.	To minimize variations and obtain consistent results regardless of the true value.
  Example	Measuring the weight of a known mass and getting a value close to the actual weight.	Measuring the weight of a known mass multiple times and getting similar results each time.
  Characteristics	Can be affected by systematic errors (bias).	Can be affected by random errors (scatter).
  Expression	Usually expressed as a percentage or in terms of absolute error.	Usually expressed as standard deviation or variance.

Some Important question from 'Unit and Measurement'

• 1. What is the SI unit of length?
• 2. Define the term "accuracy" in the context of measurements.
• 3. What is the dimensional formula of force?
• 4. Explain the difference between precision and accuracy in measurements.
• 5. Convert 5 meters per second to kilometers per hour.
• 6. Calculate the volume of a cube with sides measuring 2 meters each.
• 7. Define the term "significant figures" and explain their importance in measurements.
• 8. What is the SI unit of electric current?
• 9. Calculate the density of an object with a mass of 500 grams and a volume of 250 cubic centimeters.
• 10. Explain the concept of dimensional analysis and its importance in physics.
• 11. What is the SI unit of luminous intensity?
• 12. Calculate the kinetic energy of an object with a mass of 10 kilograms and a velocity of 5 meters per second.
• 13. Define the term "resolution" as it relates to measuring instruments.
• 14. Convert 1000 joules to kilocalories.
• 15. What is the SI unit of temperature?
• 16. Calculate the area of a rectangle with dimensions 4 meters by 6 meters.
• 17. Explain the difference between scalar and vector quantities.
• 19. Convert 50 degrees Celsius to Fahrenheit.
• 20. Define the term "standard deviation" and its role in statistical analysis of measurements.
• 21. Calculate the power output of a machine that does 5000 joules of work in 10 seconds.