Units and Measurements – JEE Mains Physics
1. Units of Measurements
- Measurement is the comparison of a physical quantity with a standard unit.
- Physical quantities like length, mass, time, etc., require proper units for measurement.
2. System of Units
- Different systems of units are used globally:
- CGS System: Centimetre, Gram, Second
- FPS System: Foot, Pound, Second
- MKS System: Metre, Kilogram, Second
- SI System: International System of Units — most widely accepted.
3. SI Units
- Established in 1960, based on seven fundamental units.
- Examples:
- Length – metre (m)
- Mass – kilogram (kg)
- Time – second (s)
- Electric current – ampere (A)
- Temperature – kelvin (K)
- Amount of substance – mole (mol)
- Luminous intensity – candela (cd)
4. Fundamental and Derived Units
- Fundamental Units: Independent of each other, like metre, kilogram, second, etc.
- Derived Units: Formed from fundamental units (e.g., velocity = metre/second, acceleration = m/s²).
5. Least Count and Significant Figures
- Least Count: The smallest measurement that an instrument can accurately measure.
- Significant Figures: Digits in a number that are reliable and necessary for accuracy.
- Rules for significant figures include:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros are not significant.
- Trailing zeros are significant if a decimal point is present.
6. Errors in Measurements
- Types of Errors:
- Systematic Errors (instrumental, environmental, observational)
- Random Errors
- Gross Errors (due to human mistakes)
- Error propagation rules when adding, subtracting, multiplying or dividing measurements.
- Absolute Error, Relative Error, Percentage Error concepts are important.
7. Dimensions of Physical Quantities
- Dimensions represent the powers to which fundamental quantities are raised to represent a physical quantity.
- Example: Force = M¹L¹T⁻²
8. Dimensional Analysis and Its Applications
- Checking correctness of physical equations (Principle of Homogeneity).
- Deriving relationships between physical quantities.
- Converting units from one system to another.
- Finding the dependence of a physical quantity on others using dimensional methods.