CHAPTER NO 1(Physical Quantities And Measurements):

• What is physics?

Physics is the branch of science that studies matter,energy,and motion.

e.g:A Falling ball.

• 1.1:Physical and Non-Physical Quantities:

• Physical Quantities: A physical quantity is a quantity that can be measured and expressed with a number  and a unit.

e.g: Length(m ),Mass(kg),Time(s)

Example sentence:The length of the table is 2 meter.

• Non-physical Quantities:

Non-physical quantities are things that cannot be measured and have no units.

e.g: Love, Honesty, Beauty,Anger

Example sentence:Happiness cannot be measured in any units.

1.2: Base and Derived Quantities:

Base Quantities: Base quantity are the fundamental physical quantities that do not depend on other quantities.

e.g:Length, Mass, Time

Example sentence :Length of a table is 2 meter.

Derived Quantities:Derived quantities are the physical quantities that are obtained by combining base.

e.g: Speed, Force,Area

Example sentence: Speed = distance ÷ time

• Measurement of a Physical Quantity:

Measure of a physical quantity means comparing an unknown quantity with a standard unit to find its value.

Example:

If the length of a table is 2 meters, it means the table’s length is twice the standard unit meter.

1.3:The International System of Units:

Definition:The International System of Units (SI) is a standard system of measurement used worldwide to measure physical quantities. It ensures that everyone uses the same units for length, mass, time, and other quantities.

Example:

• The length of a room is 5 meters.
• The mass of a bag is 2 kilograms.

Derived Units:

Definition:

Base quantities are the fundamental physical quantities that cannot be derived from any other quantity. They are measured using standard units.

Examples:

• Length – meter (m)
• Mass – kilogram (kg)
• Time – second (s)

Example in real life:

The length of a classroom is 8 meters. Here, length is a base quantity because it is measured directly.

• SI Prefixes:

Definition: SI prefixes are letters added to base units to represent multiples or fractions of that unit. They make it easier to write very large or very small numbers.

Symbols: Milli,Giga,Mega

Example in sentence:

• A pen is 15 cm long → centi = 1/100 meter.
• A city is 5 km away → kilo = 1,000 meter.

1.4:Scientific Notation:

Scientific notation is a way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10.

Form:

n = integer (positive for large numbers, negative for small numbers)

Examples:     

• Distance to Sun: 1.496 × 10⁸ km
• Mass of electron: 9.1 × 10⁻³¹ kg
• Size of bacteria: 2 × 10⁻⁶ m

1.5:Length Measuring Instruments:

• Meter Rule:

 A meter rule is a measuring instrument used to measure length or distance in meters or centimeters. It is a straight, flat, and rigid scale marked with divisions of standard units.

Example:

Measuring the length of a table → If the table is 150 cm long, we can directly read it using a meter rule.

Measuring the height of a book → Height = 25 cm

• Vernier Callipers:

A Vernier Caliper is a precise measuring instrument used to measure the length, diameter, thickness, or depth of an object. It is more accurate than a meter rule because it can measure up to 0.1 mm or 0.02 cm.

• Parts of Vernier Calliper:

Main Scale – Fixed scale marked in mm or cm.

Vernier Scale – Small sliding scale for accurate reading.

Outside Jaws – Measure external diameter or length.

Inside Jaws – Measure internal diameter.

Depth Rod – Measures depth of holes or slots.

• How to Use:

1. Place the object between the jaws.
2. Read the main scale first.
3. Read the vernier scale next for accurate measurement.
4. Add both readings for the final measurement.

• Examples:

1. External diameter of a pen → 1 cm
2. Thickness of a coin → 0.2 cm
3. Internal diameter of a pipe → 2.5 cm
4. Depth of a small hole → 1.8 cm

• Measurement using vernier callipers:

Definition:

Vernier Callipers is a precise measuring instrument used to measure small lengths, internal diameter, external diameter, and depth of objects accurately. It gives more accurate measurements than a simple ruler.

• Main Parts:

1. Main scale
2. Vernier scale
3. Outside jaws
4. Inside jaws
5. Depth rod
6. Lock screw

Procedure for Measurement:

• Place the object between the jaws of the vernier callipers.
• Note the reading on the main scale.
• Find the line on the vernier scale that exactly coincides with a line on the main scale.
• Add the main scale reading and the vernier scale reading.

Formula:

Final Reading = Main Scale Reading + Vernier Scale Reading.

Example:

• If the main scale reading is 2.3 cm and the vernier scale reading is 0.02 cm, then:
• Total measurement = 2.32 cm

Uses:

• Measuring the diameter of wires or rods.
• Measuring internal diameter of pipes.
• Measuring the depth of holes.

• 

  A stainless steel vernier caliper with engraved measurement scales, slightly open and measuring a small cylindrical object, placed on a clean white background.

  
  

Micrometer screw Gauage:

Micrometer Screw Gauge is an instrument used to measure the thickness or diameter of very small objects like wires and thin sheets very accurately.

Formula:

Final Reading = Main Scale Reading + Circular Scale Reading.

Example:

• If main scale reading = 5 mm.
• and circular scale reading = 0.28 mm.
• Then Total Reading = 5.28 mm.

Uses:

• Measuring thickness of wire.
• Measuring thin sheets.

Checking for zero Error:

Defination: Zero error occurs when the instrument shows a reading other than zero even when the jaws or spindle are fully closed.

Method:

• Close the jaws of the instrument completely.
• Check whether the zero of the main scale coincides with the zero of the vernier/circular scale.
• If the zeros do not coincide, it indicates zero error.

Correction Formula:

Correct Reading = Observed Reading − Zero Error

Measurements Using Screw Guage:

Micrometer Screw Gauge is used to measure the thickness or diameter of very small objects like wires.

Formula:

Final Reading = Main Scale Reading + Circular Scale Reading

1.7:Mass Measuring Instruments:

• Physical Balance:

Physical Balance is a mass measuring instrument used to measure the mass of an object by comparing it with standard weights.

• Working:

The object is placed on one pan and standard weights are placed on the other pan. When both pans become balanced, the mass of the object is equal to the total standard weights used.

1.7:Time Measuring Instruments:

• Stopwatch:

Stopwatch is a time measuring instrument used to measure short intervals of time with accuracy, such as in experiments, sports, or reaction time studies.

Main Features:

• Has a start, stop, and reset button.
• Can measure seconds and fractions of a second.
• Comes in Normal, Small, and Large sizes depending on use.

Uses:

• Measuring time in laboratory experiments.
• Timing races or sports events.
• Recording reaction times.

  

  A digital stopwatch displaying elapsed time, held in a hand with a blurred running track in the background.

  
  

1.8:Volume Measuring Instruments:

Measuring Cylinder:

Measuring Cylinder is a volume measuring instrument used to measure the volume of liquids accurately.

Example: Measuring 50 mL of water for an experiment.

• Displacement Can Method:

Displacement Can measures the volume of irregular solids by collecting the water overflowed when the object is placed in it.

Example: Measuring the volume of a stone.

1.9:Errors in Measurements:

Errors in measurement occur when the measured value differs from the true value of a quantity. They are unavoidable but can be minimized.

Types of Errors:

• Human Error:

Mistakes made by the person measuring, such as reading the scale incorrectly or misplacing the instrument.

Example: Misreading the vernier scale by 0.1 cm.

• Systematic Error:

Errors caused by faulty instruments, improper calibration, or consistent procedural mistakes. These errors are reproducible.

Example: A balance that always shows 0.5 g more than the actual mass.

• Random Error:

Errors caused by unpredictable and uncontrollable factors, like slight vibrations, temperature changes, or human reaction time.

Example: Slight fluctuations in time measured by a stopwatch.

1.10:Uncertainty in Measurement:

Uncertainty in measurement is the doubt about the exactness of a measured value. It tells us how much the measured value may differ from the true value.

Example:

If a length is measured as 10.2 ± 0.1 cm, the 0.1 cm represents the uncertainty.

It is not an error, but a way to show precision and reliability of the measurement.

1.11:Significant Figures (SF):

Significant figures are the meaningful digits in a measurement that indicate its accuracy and precision. They include:

• All non-zero digits.
• Any zeros between non-zero digits.
• The first uncertain digit.

Example:

• Measurement = 0.05230 m.
• 5, 2, 3 → meaningful digits.
• 0 at the end after 3 → significant .because it shows precision
• Total 4 significant figures.

Uses:

• To show the accuracy of measurements.
• To avoid false precision in calculations.

• 

  An educational diagram showing a ruler measurement with highlighted significant figures, distinguishing certain and estimated digits.

  
  

1.12:Precision and Accuracy:

• Accuracy: Accuracy refers to how close a measured value is to the true or accepted value. High accuracy means the measurement is very near to the real value.

Example: Measuring a 10 cm rod and getting 9.98 cm is highly accurate.

• Precision: Precision refers to how closely repeated measurements agree with each other, regardless of whether they are near the true value or not. High precision means measurements are consistent.

Example: Measuring a 10 cm rod three times and getting 9.80 cm, 9.81 cm, 9.79 cm is precise.

1.13:Rounding of Digits:

Rounding of digits means approximating a number to a required number of significant figures or decimal places.

Example: 12.768 → 12.77 (rounded to 2 decimal places).