NEET Physics: Waves – NCERT Masterclass & 100 MCQ Quiz

UNITS AND MEASUREMENT

Detailed Physics Module for NEET Excellence

1. The Need for Measurement

Physics is a quantitative science based on the measurement of physical quantities. To measure a physical quantity, we need a standard of reference, which is internationally accepted. This standard is called a Unit. Any measurement consists of two parts: a numerical value (magnitude) and a unit.

• Base Units: Units of fundamental quantities (Length, Mass, Time, etc.) that cannot be derived from one another.
• Derived Units: Units of physical quantities that can be expressed as a combination of base units (e.g., Velocity, Force).

2. Systems of Units & The SI System

Historically, scientists used the CGS (centimetre, gram, second), FPS (foot, pound, second), and MKS (metre, kilogram, second) systems. To standardize global science, the Système Internationale (SI) was introduced.

🔹 The 7 Base Units

1. Length: metre (m)
2. Mass: kilogram (kg)
3. Time: second (s)
4. Electric Current: ampere (A)
5. Temperature: kelvin (K)
6. Amount of Substance: mole (mol)
7. Luminous Intensity: candela (cd)

🔹 Supplementary Units

There are two quantities that have units but are purely dimensionless:

• Plane Angle (dθ): Ratio of arc length to radius. Unit: radian (rad).
• Solid Angle (dΩ): Ratio of intercepted area to the square of radius. Unit: steradian (sr).

3. Significant Figures

Significant figures tell us about the precision of a measurement. It includes all perfectly reliable digits plus the first uncertain digit.

📌 Rules for Counting Significant Figures:

• All non-zero digits are significant (e.g., 42.3 has 3).
• Zeros between non-zero digits are significant (e.g., 5.004 has 4).
• Leading zeros are never significant (e.g., 0.0045 has 2).
• Trailing zeros without a decimal point are not significant (e.g., 1500 has 2).
• Trailing zeros with a decimal point are significant (e.g., 3.500 has 4).

🔹 Rules for Arithmetic Operations

Multiplication/Division: The final result must have the same number of significant figures as the original number with the least significant figures.

Addition/Subtraction: The final result must have the same number of decimal places as the original number with the least decimal places.

4. Errors in Measurement

No measurement is perfectly accurate. The difference between the true value and the measured value is called an error.

• Absolute Error (Δa): The magnitude of the difference between the true value and the individual measured value.
• Relative Error: The ratio of the mean absolute error to the mean value (Δa_mean / a_mean).
• Percentage Error: Relative error expressed in percentage.

Combination of Errors:
If $Z = \frac{A^p \cdot B^q}{C^r}$
Max Percentage Error = $p\left(\frac{\Delta A}{A}\right)\% + q\left(\frac{\Delta B}{B}\right)\% + r\left(\frac{\Delta C}{C}\right)\%$

5. Dimensions of Physical Quantities

The dimensions of a physical quantity are the powers to which the base quantities are raised to represent that quantity. We use square brackets: [M] for mass, [L] for length, [T] for time.

Example: Force = Mass × Acceleration = $[M] \times [L T^{-2}] = [M L T^{-2}]$.

🔹 Principle of Homogeneity of Dimensions

We can only add or subtract physical quantities that have the exact same dimensions. If x = A + B, then dimensionally [x] = [A] = [B].

Applications: 1. Checking correctness of an equation. 2. Deriving relations between physical quantities. 3. Converting units from one system to another.

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🚀 NEET UNITS & MEASUREMENT MEGA QUIZ (100 MCQ)

Solve the 5 parts below to master Dimensions, Errors, and Significant Figures.