Watch Video
What Are the Different Types of Units in Measurement?
The Units And Measurement chapter is the essential starting point for every aspiring JEE candidate. It builds the foundation for all physical sciences by introducing how physical quantities are defined, measured, and compared using standard units. Understanding this topic ensures you approach Physics and Chemistry confidently, laying the groundwork for advanced concepts and problem-solving.
Fundamental Forces and Their Ranges
Nature is governed by four fundamental forces: gravitational, electromagnetic, strong nuclear, and weak nuclear. Gravitational force is the weakest but has infinite range, affecting all masses in the universe. Electromagnetic force acts between charged particles, combining electric and magnetic effects. The strong nuclear force binds protons and neutrons, dominating within the nucleus and having a very short range about 10−15 m. The weak nuclear force operates in nuclear processes like beta decay and has a range around 10−16 m.
Physical Quantities and Their Classifications
Physical quantities describe measurable attributes and are classified as fundamental or derived. Fundamental (base) quantities such as mass, length, time, temperature, current, luminous intensity, and amount of substance are independent. Derived quantities like area, force, and density are expressed using these base quantities. Clarity on classifications is crucial for units and measurements class 11 and standard chart construction.
Dimensions and Dimensional Formula
The dimension of a physical quantity denotes the powers to which base units are raised to represent it. For example, mass has the dimensional formula [M1L0T0], while force is [M1L1T−2]. Dimensional equations equate a quantity to its dimensional formula. Understanding this, as covered in units and measurements class 11 pdf notes, is key for exam questions.
Rules of Dimensions and Dimensionless Quantities
Only physical quantities with the same dimensions can be added or subtracted. Dimensionless quantities include ratios of physical quantities with the same units, mathematical constants, and values of standard mathematical functions. Dimensional analysis provides a powerful way to verify equations throughout units and measurements.
Conversion Between Systems of Units
Physical quantities may be expressed in different units such as SI, CGS, or other systems. The value remains constant, but the numerical value and unit change. Conversion is accomplished using dimensional formulas, ensuring values are always expressed in correct units for class 11 questions and answers.
Law of Homogeneity and Applications of Dimensional Analysis
The law of homogeneity states that all terms in a physical equation must have the same dimensions. This principle helps verify equations and derive formulas relating physical quantities, as emphasized in many units and measurements questions and answers pdfs.
Limitations of Dimensional Analysis
Dimensional analysis cannot derive formulas involving more than three basic quantities, summations, or functional forms like exponentials and trigonometric expressions. It cannot provide dimensionless constants and cannot distinguish between scalar and vector quantities. Being aware of these limits is crucial when using dimensional reasoning in exams.
Significant Figures, Rounding Off, and Order of Magnitude
Significant figures (SF) indicate the precision of measured values. The more SFs, the higher the accuracy. Rules for counting SFs, and for rounding off, help reduce computational errors. Order of magnitude provides a quick comparison by expressing values as powers of ten, a technique common in units and measurements chemistry and physics.
Types and Representation of Errors in Measurement
Measurements always involve errors due to instruments, environment, or human mistakes. Systematic errors have identifiable causes and can often be corrected. Random errors are unpredictable, while gross errors arise from mistakes or carelessness. Recognizing error types is especially important for MCQ problems in units and measurements class 11 ncert solutions.
Quantifying Errors and Calculating Uncertainty
Absolute error is the difference between the measured and true values. Mean absolute error provides an average estimate. Relative (fractional) and percentage errors define error size compared to the measured value—a common exam question. Least count error is determined by the resolution of the instrument used for measurement.
Error Propagation Rules
For addition and subtraction, maximum absolute error is the sum of individual errors. For multiplication and division, relative errors are summed. When a measured quantity is raised to a power, the fractional error is multiplied by the exponent, allowing accurate evaluation of error propagation in formulas.
Vernier Callipers: Principle and Usage
A vernier calliper is used for precise linear measurements over small ranges, such as diameters of objects. Its least count is typically 0.1 mm, calculated using differences between main scale and vernier scale readings. Correcting for positive or negative zero errors is vital for accurate results, a key focus in units and measurements class 11 notes.
Screw Gauge: Measuring with Precision
A screw gauge offers even higher precision, used mainly for the dimensions of small and thin objects. Pitch is the distance advanced per full rotation, and least count is pitch divided by number of scale divisions. Proper adjustment for zero error is needed to ensure accuracy. Many units and measurements class 11 pdf download notes cover these details for test practice.
Spherometer and Its Components
The spherometer measures the curvature or thickness of spherical surfaces. It has a main scale and a circular scale; their combined use allows extremely fine measurements. Least count is calculated as pitch divided by number of divisions on the circular scale, supporting experimental questions in units and measurements class 11 questions answers.
Accuracy Versus Precision in Measurements
Accuracy describes how closely a measurement matches the true value, while precision reflects the consistency across repeated measurements. High precision does not guarantee accuracy, as systematic errors may bias results—a crucial distinction for all experimental work and advanced problem-solving.
Solved Example 1: Dimensional Analysis and the Argument of Functions
Consider the formula U = p cos(qt + 6π) where U is potential energy and t is time. Since the cosine function takes a dimensionless argument, qt must be dimensionless, giving q the dimension [T−1]. Both U and p have the dimensions of energy, [M1L2T−2].
Solved Example 2: Using Dimensional Analysis for Derivation
A satellite's orbital period T depends on the gravitational constant G, Earth’s mass M, and orbital radius R. Assume T ∝ GaMbRc. Solving the dimensional equation gives a = −1/2, b = −1/2, c = 3/2, resulting in T proportional to R3/2 divided by (GM)1/2. This technique quickly predicts formula form for challenging questions.
Solved Example 3: Unit Conversion Between SI and CGS
To convert 1 Newton (SI) to dyne (CGS): 1 N = 1 kg·m/s2 = 1,000 g × 100 cm/s2 = 100,000 dyne. The answer is 1 N = 105 dyne.
Solved Example 4: Zero Error in Vernier Calliper Measurement
If the main scale reading is zero, the vernier scale division aligning is 3, and the least count is 0.1 mm, then zero error is 0 + (3 × 0.1) = 0.3 mm.
Solved Example 5: Screw Gauge Diameter Calculation
A screw gauge with a 1 mm pitch and 100 circular scale divisions measures a linear scale reading of 6 and a circular scale reading of 40. Least count = 1/100 = 0.01 mm. The total diameter = 6 mm + (40 × 0.01 mm) = 6.4 mm.
Summary Table: SI Fundamental and Derived Units
| Quantity | SI Unit (Symbol) |
|---|---|
| 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) |
Exam Tips for Units and Measurements
Always check for dimensional consistency in every formula. Use SI units unless the problem specifies otherwise. For error calculations, remember to use relative or percentage errors, not just absolute errors. Convert units carefully, especially when moving between cm², cm³ and m², m³. Mastery in these basics reflects in strong problem-solving skills for all physics and chemistry concepts.
Vedantu Resources and Next Steps
Consistent practice with official materials is the key to scoring high. Use Vedantu’s comprehensive units and measurements mock test 2 and regularly review solved examples. For conceptual bridges and detailed dimensional checks, refer to the kinematics overview and dimensions of displacement guides.
Where to Practice and Revise Further
Enhance your grip over units and measurements class 11 by solving more advanced problems and reviewing NCERT solutions. Vedantu also provides targeted mock tests in this topic and next-level study material to ensure full clarity before exams.
- Understand practical significance of error minimization.
- Solve more questions from units and measurements class 11 pdf notes.
- Always verify units in calculations and conversions.
- Apply dimensional checks on derived formulas.
- Master all error rules for fraction, sum, and product operations.
Understanding Units and Measurement
ShareFAQs on Understanding Units and Measurement
1. What is measurement in physics?
Measurement in physics refers to the quantitative comparison of a physical quantity with a standard unit. It helps in expressing a physical quantity with both a number and a unit.
- It ensures standardization and accuracy in scientific observations.
- Measurements require a defined unit and a suitable measuring instrument.
- Common quantities include length, mass, and time, each with its standard unit.
2. What are the fundamental and derived units?
Fundamental units are the basic units from which other units are derived, while derived units are formed by combining fundamental units.
- Examples of fundamental units: metre (length), kilogram (mass), second (time).
- Examples of derived units: newton (force), joule (energy), which are formed from fundamental units.
3. What is meant by the International System of Units (SI)?
The International System of Units (SI) is the globally accepted system for measuring physical quantities.
- It consists of seven fundamental units like metre, kilogram, second, ampere, kelvin, mole, and candela.
- SI units ensure consistency and universal understanding in science.
4. Why are significant figures important in measurements?
Significant figures represent the digits in a measurement that are reliable and necessary to indicate uncertainty.
- They show the precision of a measured value.
- Only meaningful digits and the first uncertain digit are significant.
- For example, in 12.30, all four digits are significant.
5. How is accuracy different from precision in measurements?
Accuracy indicates how close a measured value is to the true value, while precision reflects the closeness among repeated measurements.
- Accurate measurements are close to the accepted value.
- Precise measurements have little variation; they may or may not be accurate.
6. What are the types of errors in measurement?
Errors in measurement are the differences between a measured value and the true value. They are classified as:
- Systematic errors: Consistent and predictable errors, e.g., instrument error.
- Random errors: Irregular variations, e.g., fluctuations in readings.
- Gross errors: Due to human mistakes or carelessness.
7. What are the seven fundamental quantities in physics?
The seven fundamental quantities according to SI units are:
- 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)
8. How are physical quantities expressed?
A physical quantity is expressed as the product of its numerical value and its unit.
- For example: Distance = 5 m, where 5 is the number and 'm' is the unit.
- This helps in standardising and comparing different measurements.
9. Why is dimensional analysis useful?
Dimensional analysis is a method to check the correctness of equations and to convert units.
- It involves expressing quantities in terms of their basic dimensions (M, L, T).
- It helps in verifying the consistency of physical equations.
- Allows conversion between different unit systems.
10. What are the rules for writing significant figures?
The rules for writing significant figures ensure clarity and precision in reporting measurements.
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros are not significant.
- Trailing zeros in a decimal number are significant.
