Measurements and Units

Measurement is the process of finding the size, quantity, or degree of something. In Physics, accurate measurement is crucial for understanding the physical world.

1. Fundamental and Derived Quantities

Fundamental Quantities: These are basic physical quantities that do not depend on other quantities. There are seven basic fundamental quantities in the SI system:

• Mass (Kilogram, kg)
• Length (Metre, m)
• Time (Second, s)
• Electric Current (Ampere, A)
• Temperature (Kelvin, K)
• Amount of Substance (Mole, mol)
• Luminous Intensity (Candela, cd)

Derived Quantities: These are quantities obtained by the combination of fundamental quantities through multiplication or division. Examples include:

• Area (Length x Length) = m²
• Volume (Length x Length x Length) = m³
• Velocity (Displacement / Time) = m/s
• Force (Mass x Acceleration) = kg.m/s² (Newton)

2. Measuring Instruments

Length

• Metre Rule: Accuracy of 0.1 cm (1 mm). Used for general lengths.
• Vernier Calipers: Accuracy of 0.01 cm (0.1 mm). Used for internal/external diameters of tubes and depth.
• Micrometer Screw Gauge: Accuracy of 0.01 mm (0.001 cm). Used for very small diameters like wires.

Mass and Time

• Beam Balance: Measures mass by comparing an unknown mass with a known mass.
• Stopwatch/Stopclock: Measures time intervals. Digital stopwatches are more precise than analog ones.

3. Dimensions of Physical Quantities

Dimensions describe the physical nature of a quantity. The symbols used are [M] for mass, [L] for length, and [T] for time.

• Velocity: [L][T]⁻¹
• Acceleration: [L][T]⁻²
• Force: [M][L][T]⁻²
• Work/Energy: [M][L]²[T]⁻²

Dimensional Homogeneity: An equation is physically correct only if the dimensions of all terms on both sides are the same.

4. Errors and Accuracy

• Significant Figures: The number of digits that carry meaning contributing to its measurement resolution.
• Standard Form: Expressing numbers as a × 10ⁿ, where 1 ≤ a < 10.
• Random Errors: Caused by unpredictable fluctuations.
• Systematic Errors: Caused by faulty instruments (e.g., zero error).

5. Distance and Displacement

Distance: A scalar quantity representing the total path covered.

Displacement: A vector quantity representing the shortest distance between an initial and final position in a specific direction.