MHT CET EXAM NOTES

1. Measurements – MHT-CET Revision Notes

1. Introduction to Measurement

Measurement is the process of comparing a physical quantity with a standard unit.

Every measurement consists of two parts: numerical value (magnitude) and unit of measurement.

Example: In "5 meters," 5 is the magnitude, and meter (m) is the unit.

2. Fundamental and Derived Quantities

Fundamental Quantities (Basic Physical Quantities)

There are seven fundamental quantities in physics:

Length (meter, m)

Mass (kilogram, kg)

Time (second, s)

Temperature (kelvin, K)

Electric Current (ampere, A)

Luminous Intensity (candela, cd)

Amount of Substance (mole, mol)

Derived Quantities (Obtained from Fundamental Quantities)

Some examples:

Area (square meter, m²) = Length × Breadth

Volume (cubic meter, m³) = Length × Breadth × Height

Velocity (meter per second, m/s) = Distance / Time

Acceleration (meter per second², m/s²) = Velocity / Time

Force (newton, N) = Mass × Acceleration

Work (joule, J) = Force × Displacement

Power (watt, W) = Work / Time

3. Systems of Units

Different systems of measurement:

CGS System: Uses centimeter (cm), gram (g), and second (s).

MKS System: Uses meter (m), kilogram (kg), and second (s).

FPS System: Uses foot (ft), pound (lb), and second (s).

SI System (International System): Modern system based on the MKS system.

4. Dimensional Analysis

Dimensional analysis helps in checking the correctness of equations and converting units.

Dimensional Formulas of Some Physical Quantities:

Velocity: [M⁰L¹T⁻¹]

Acceleration: [M⁰L¹T⁻²]

Force: [M¹L¹T⁻²]

Work/Energy: [M¹L²T⁻²]

Power: [M¹L²T⁻³]

Pressure: [M¹L⁻¹T⁻²]

Momentum: [M¹L¹T⁻¹]

Principle of Homogeneity

The dimensions on both sides of a physical equation must be the same. This is used to check if an equation is correct.

Example: Checking the Equation for Force

We know Force (F) = Mass × Acceleration

Mass (M) → [M¹]

Acceleration (a) → [M⁰L¹T⁻²]

So, Force = [M¹] × [L¹T⁻²] = [M¹L¹T⁻²]
Since both sides match, the equation is dimensionally correct.

5. Errors in Measurement

Errors occur due to limitations in instruments, human mistakes, or environmental factors.

Types of Errors:

1. Systematic Errors – Constant errors due to instrumental defects, external conditions, or observer bias.

2. Random Errors – Occur unpredictably due to external disturbances or limitations in human observation.

3. Gross Errors – Mistakes in using instruments, such as wrong readings.

4. Absolute Error – Difference between the measured value and the true value.

5. Relative Error – Ratio of absolute error to true value.

6. Percentage Error – Relative error expressed as a percentage.

Error Formulae

Absolute Error = |Measured Value - True Value|

Relative Error = Absolute Error / True Value

Percentage Error = (Relative Error × 100)%

6. Significant Figures

Significant figures represent the precision of a measured value.

Rules for Counting Significant Figures:

All non-zero digits are significant. Example: 123 has 3 significant figures.

Zeros between non-zero digits are significant. Example: 102 has 3 significant figures.

Leading zeros are NOT significant. Example: 0.002 has 1 significant figure.

Trailing zeros are significant ONLY if there is a decimal point. Example: 5.00 has 3 significant figures.

Rules for Rounding Off:

1. If the digit to be removed is less than 5, the preceding number remains unchanged. Example: 4.32 rounded to two significant figures is 4.3.

2. If the digit to be removed is 5 or greater, the preceding number increases by 1. Example: 4.37 rounded to two significant figures is 4.4.

7. Applications of Measurements in Physics

Scientific Research: Accurate measurements are crucial in experiments.

Engineering & Technology: Used in designing machinery, buildings, and electronics.

Medical Field: Measurements of temperature, blood pressure, and weight are critical.

Space & Aviation: Precise calculations are needed for satellite launches and navigation.

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