📘 Full Notes (Physical Quantities and Measurements)
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Introduction to Physical Quantities and Measurements
The study of physical quantities and measurements forms the foundation of physics. It deals with how quantities are defined, measured, and expressed using standard units and instruments.
In everyday life and science, accurate measurement is essential. From measuring the length of a pencil to determining the mass of a planet, every observation in physics depends on precise measurements of physical quantities.
This chapter introduces physical quantities, units, prefixes, and measuring instruments such as metre rules, vernier callipers, and micrometers. It also explains how to measure with accuracy, identify least count, and understand possible errors.
Key Concepts Covered
- Physical quantities and their parts
- Base and derived quantities
- SI units and prefixes
- Measurement and accuracy
- Least count and zero error
- Use of vernier callipers and micrometer screw gauge
- Types of errors in measurement
- Difference between precision and accuracy
Important Definitions
Physical Quantity: A quantity that can be measured and expressed in terms of a number and a unit, such as length, mass, and time.
Measurement: The process of comparing an unknown quantity with a known standard quantity of the same kind.
Base Quantities: Fundamental physical quantities that are independent of others, such as length, mass, and time.
Derived Quantities: Quantities that are derived from base quantities through mathematical relationships, such as area, volume, and speed.
SI Units: The internationally accepted system of units known as the Système International d’Unités (SI).
Least Count: The smallest value that can be measured accurately by an instrument.
Zero Error: The error that occurs when the zero mark of the instrument does not coincide with the reference line when no measurement is being taken.
Key Formulas
Least Count of Vernier Callipers
\[\text{Least Count} = \text{Value of 1 main scale division} - \text{Value of 1 vernier scale division}\]Least Count of Micrometer Screw Gauge
\[\text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}}\]Measured Value
\[\text{Measured Value} = \text{Main Scale Reading} + (\text{Vernier Division Coinciding} \times \text{Least Count})\]Density
\[\rho = \frac{m}{V}\]Where \( \rho \) is density, \( m \) is mass, and \( V \) is volume.
Detailed Chapter Content
1. Physical Quantities and Their Parts
Each physical quantity consists of two parts — a numerical value and a unit. For example, in “5 m”, 5 is the numerical value and metre (m) is the unit.
2. Base and Derived Quantities
There are seven base quantities in the SI system. All other physical quantities are derived quantities obtained from these base quantities through mathematical relationships.
3. Prefixes
Prefixes are used to express very large or very small quantities conveniently. For example:
4. Measuring Instruments
The instruments commonly used for measuring length, diameter, and thickness include:
- Metre rule or scale: Measures objects with least count of 1 mm.
- Vernier callipers: Measures internal/external diameters and depth with least count of 0.01 cm.
- Micrometer screw gauge: Measures very small thickness with least count of 0.01 mm.
5. Zero Error and Its Correction
If the zero mark of an instrument does not coincide with the reference line, a zero error occurs. It is corrected by subtracting or adding the zero error from the measured reading depending on whether it is positive or negative.
6. Errors in Measurement
Errors are unavoidable in measurements. They are of three types:
- Human Error: Due to carelessness or parallax in reading scales.
- Systematic Error: Caused by faulty instruments or calibration.
- Random Error: Due to unknown or unpredictable variations.
7. Precision and Accuracy
Precision refers to the closeness of repeated measurements to each other, while accuracy refers to the closeness of a measurement to the true value. A result may be precise without being accurate.
8. Significant Figures
Significant figures indicate the precision of a measurement. They include all certain digits and one uncertain (estimated) digit.
Created by Hira Science Academy | Aligned with PECTA 2025 Syllabus