Introduction
Have you ever wondered how we know the exact distance between Delhi and Mumbai? Or how doctors measure your body temperature accurately? Or how shopkeepers weigh vegetables precisely? The answer lies in the science of measurement - the foundation of all scientific discovery and technological progress.
Physics begins with measurement. Before we can understand motion, energy, or electricity, we need to know how to measure things accurately. This might seem simple, but it's one of the most important topics in physics and appears in almost every competitive exam.
For students preparing for UPSC, SSC, Railways, or Delhi Police exams, mastering units and measurements is crucial because:
1. It forms the base for all physics concepts
2. It's directly asked in General Science sections
3. It helps in solving numerical problems in other topics
4. It connects to real-life applications you see every day
In this comprehensive guide, we'll
break down this fundamental topic into simple, easy-to-understand sections with
practical examples that will help you remember concepts for your exams.
What are Physical Quantities?
Physical quantities are those quantities that can be measured and expressed in numbers with units. Any meaningful term which can be measured is a physical quantity. For example, when we measure the length of a road, the weight of a person, or the time taken to complete a task, we are dealing with physical quantities.
Examples of Physical Quantities:
· Length of a table: 2 meters
· Mass of a book: 500 grams
· Time for cooking: 30 minutes
· Temperature of water: 100 degrees Celsius
· Speed of a car: 60 kilometers per hour
All these quantities have two parts: a number (numerical value) and a unit. Without units, the measurement is meaningless. If someone says "the distance is 5," you cannot understand whether it is 5 meters, 5 kilometers, or 5 centimeters.
Types of Physical Quantities
Physical quantities are divided into two main categories: Fundamental Quantities and Derived Quantities.
Fundamental (Base) Quantities
Fundamental quantities are basic quantities that cannot be expressed in terms of other quantities. They are independent and form the foundation of all measurements. The International System of Units (SI) has seven fundamental quantities.
Table: Seven Fundamental Quantities and Their SI Units
|
Sr. No. |
Physical Quantity |
SI Unit |
Symbol |
|
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 |
Example: When we measure the length of a pencil as 15 centimeters, we are using the fundamental quantity "length" with the base unit "meter" (1 meter = 100 centimeters).
Memory Trick: To remember all 7, use the phrase:
"Little Men Take
Apples, Keep Making Candies"
· L - Length
· M - Mass
· T - Time
· A - Electric Current
· K - Temperature
· M - Amount of Substance
· C - Luminous Intensity
Derived Quantities
Derived quantities are obtained by combining two or more fundamental quantities using mathematical operations. These quantities depend on fundamental quantities.
Table: Common Derived Quantities
|
Derived Quantity |
Formula |
SI Unit |
Symbol |
|
Area |
Length × Length |
Square metre |
m² |
|
Volume |
Length × Length × Length |
Cubic metre |
m³ |
|
Speed/Velocity |
Distance ÷ Time |
Metre per second |
m/s |
|
Acceleration |
Velocity ÷ Time |
Metre per second² |
m/s² |
|
Force |
Mass × Acceleration |
Newton |
N (kg·m/s²) |
|
Pressure |
Force ÷ Area |
Pascal |
Pa (N/m²) |
|
Work/Energy |
Force × Distance |
Joule |
J (N·m) |
|
Power |
Work ÷ Time |
Watt |
W (J/s) |
Example: To find the speed of a train, we divide distance (length) by time. If a train travels 120 kilometers in 2 hours, its speed is 120 ÷ 2 = 60 km/hour.
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scalar quantities
Scalar quantities are physical quantities that have only magnitude (size) and no direction. You can describe them completely just by a number and a unit.
They follow simple arithmetic rules in addition and subtraction.
Example statements:
o “The mass of the book is 2 kg.”
o “The temperature is 30 °C.”
Common examples of scalar quantities:
· Mass
· Time
· Distance
· Speed
· Temperature
· Energy
· Work
· Volume
· Density
What are vector quantities?
Vector quantities are physical quantities that have both magnitude and direction. To describe them fully, you must mention “how much” and “in which direction”.
They are often represented by arrows: length of arrow = magnitude, arrowhead = direction.
Vector addition follows special rules (triangle or parallelogram law), not simple plus-minus.
Common examples of vector quantities:
· Displacement
· Velocity
· Acceleration
· Force
· Momentum
· Weight
· Electric field
· Magnetic field
Quick comparison table:
|
Property |
Scalar Quantity |
Vector Quantity |
|
Definition |
Has only magnitude |
Has magnitude and direction |
|
Representation |
Number + unit (e.g., 10 s) |
Arrow or bold symbol with direction (e.g., velocity to east) |
|
Direction |
Not required |
Essential |
|
Examples |
Mass, time, speed, energy, temperature |
Displacement, velocity, force, acceleration |
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Unit
A unit is a fixed quantity used as a standard for measurement. It helps us compare and express physical quantities. For example, when we say a room is 5 meters long, "meter" is the unit of length.
Properties of a Good Unit
A standard unit should have these characteristics:
· Well-defined: The concept should be clear and understandable
· Suitable size: Neither too large nor too small for practical use
· Easily reproducible: Can be created anywhere in the world
· Unchangeable: Does not change with time, place, or physical conditions like temperature and pressure
· Easily accessible: Available for use when needed
Example: The meter is a good unit because it is clearly defined, easy to reproduce with measuring tapes and scales, and remains constant everywhere.
Systems of Units
Over time, different systems of units were developed for measurement.
CGS System
CGS stands for Centimeter-Gram-Second system.
· Length: Centimeter (cm)
· Mass: Gram (g)
· Time: Second (s)
This system was commonly used in older physics books and some scientific calculations.
FPS System
FPS stands for Foot-Pound-Second system.
· Length: Foot (ft)
· Mass: Pound (lb)
· Time: Second (s)
This system is still used in some countries like the United States.
MKS System
MKS stands for Meter-Kilogram-Second system.
· Length: Meter (m)
· Mass: Kilogram (kg)
· Time: Second (s)
This system became the foundation for the modern SI system.
SI System (International System of Units)
The SI system is the modern and most widely used system of measurement in the world. It is based on seven base units and is accepted internationally.
Example: If you measure the height of a building as 30 meters in SI units, it would be 3000 centimeters in CGS units and approximately 98.4 feet in FPS units.
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Measuring Instruments
Measuring instruments are devices used to measure physical quantities accurately. Different instruments are used for different quantities.
Instruments for Measuring Length
1. Meter Scale/Ruler
· Used for measuring length up to 1 meter or 100 centimeters
· Least count: 1 millimeter (0.1 cm)
· Example: Measuring the length of a notebook, pencil, or table
2. Vernier Caliper
· Used for measuring small lengths, thickness, and diameter with high accuracy
· Least count: 0.1 millimeter (0.01 cm)
· Example: Measuring the diameter of a coin, thickness of a glass sheet
3. Screw Gauge (Micrometer)
· Used for measuring very small lengths and thickness
· Least count: 0.01 millimeter (0.001 cm)
· Example: Measuring the thickness of a wire, paper, or thin metal sheet
4. Measuring Tape
· Used for measuring larger lengths
· Available in lengths of 2 meters, 5 meters, 10 meters, etc.
· Example: Measuring the length of a room, height of a building
Instruments for Measuring Mass
1. Physical Balance
· Used in laboratories for accurate measurement of mass
· Example: Measuring the mass of chemicals in a lab
2. Weighing Machine
· Used for measuring body weight and heavy objects
· Example: Measuring your body weight, luggage weight
3. Spring Balance
· Used to measure force and weight
· Example: Measuring the weight of fruits, vegetables in markets
Instruments for Measuring Time
1. Stopwatch
· Used for measuring short time intervals
· Can measure time in seconds and fractions of seconds
· Example: Measuring the time taken to run 100 meters, chemical reaction time
2. Clocks and Watches
· Used for measuring time in hours, minutes, and seconds
· Example: Daily time measurement
3. Pendulum Clock
· Uses the regular motion of a pendulum
· Example: Wall clocks in homes and offices
Instruments for Measuring Temperature
1. Thermometer
· Used to measure temperature
· Different types: Clinical thermometer, laboratory thermometer, digital thermometer
· Example: Measuring body temperature (clinical), water temperature (lab)
2. Pyrometer
· Used to measure very high temperatures
· Example: Measuring temperature in furnaces, molten metals
Other Important Instruments
Table: Measuring Instruments and Their Uses
|
Instrument |
Measures |
Example Use |
|
Ammeter |
Electric current |
Measuring current in a circuit |
|
Voltmeter |
Electric voltage |
Measuring voltage across a battery |
|
Barometer |
Atmospheric pressure |
Weather forecasting |
|
Hydrometer |
Density of liquids |
Testing battery acid, milk quality |
|
Speedometer |
Speed of vehicles |
Car, bike speed measurement |
Measurement and Its Importance
Measurement is the process of comparing an unknown quantity with a known standard quantity (unit). Accurate measurement is essential in science, engineering, medicine, trade, and daily life.
Least Count of an Instrument
The least count is the smallest value that can be measured by an instrument. It determines the precision of the instrument.
Examples:
· Meter scale: Least count = 1 mm
· Vernier caliper: Least count = 0.1 mm
· Screw gauge: Least count = 0.01 mm
A smaller least count means higher precision and accuracy.
Errors in Measurement
When we measure any physical quantity, some errors may occur. Understanding errors is important for accurate results.
Types of Errors:
1. Systematic Errors: Occur due to faulty instruments or improper technique
2. Random Errors: Occur due to unpredictable changes during measurement
3. Personal Errors: Occur due to human mistakes in reading or recording
Example: If a weighing machine shows 1 kg when nothing is placed on it, all measurements will have a systematic error of +1 kg.
Unit Conversion
Converting units from one system to another is an important skill for competitive exams. You must know the basic conversion factors.
Table: Important Unit Conversions
|
Conversion |
Value |
|
1 kilometer |
1000 meters |
|
1 meter |
100 centimeters |
|
1 meter |
1000 millimeters |
|
1 kilogram |
1000 grams |
|
1 hour |
60 minutes |
|
1 minute |
60 seconds |
|
1 km/hour |
5/18 m/second |
Example:
Convert 72 km/hour to m/second.
Solution: 72 km/hour = 72 × (5/18) = 20 m/second
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Dimensional Analysis
Dimensions represent the powers to which fundamental quantities are raised in a physical quantity. Dimensional analysis helps check the correctness of equations and derive relationships.
Dimensional Formula Notation:
· Length: [L]
· Mass: [M]
· Time: [T]
Examples:
· Area = Length × Length = [L] × [L] = [L²]
· Velocity = Distance ÷ Time = [L] ÷ [T] = [LT⁻¹]
· Force = Mass × Acceleration = [M] × [LT⁻²] = [MLT⁻²]
Frequently Asked Questions (FAQs)
Q1: What is the difference between
fundamental and derived quantities?
Fundamental quantities are independent basic quantities (like length, mass,
time), while derived quantities are obtained by combining fundamental
quantities (like speed, force, energy).
Q2: Why is the SI system preferred
over other systems?
The SI system is universally accepted, easier to use with decimal-based
conversions, and ensures consistency in scientific work worldwide. All
competitive exams use SI units.
Q3: What is the least count of a
measuring instrument?
The least count is the smallest measurement that an instrument can accurately
measure. For example, a regular ruler has a least count of 1 mm.
Q4: How many fundamental units are
there in the SI system?
There are seven fundamental units in the SI system: meter (m), kilogram (kg),
second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
Q5: What instruments are used to
measure very small lengths?
Vernier caliper (least count 0.1 mm) and screw gauge/micrometer (least count
0.01 mm) are used to measure small lengths accurately.
Q6: Why do we need standard units?
Standard units ensure that measurements are consistent, comparable, and
understood by everyone across the world. They eliminate confusion in
scientific, commercial, and daily activities.
Q7:
What is the SI unit of temperature?
The SI unit of temperature is Kelvin (K). However, Celsius (°C) is commonly
used in daily life. The conversion is: K = °C + 273.15.
Q8: Which measuring instrument is most
accurate for measuring wire thickness?
A screw gauge (micrometer) is most accurate for measuring wire thickness as it
has the smallest least count of 0.01 mm.
Q9: What are supplementary units in SI
system?
Radian (rad) for measuring plane angles and steradian (sr) for measuring solid
angles are the two supplementary units in the SI system.
Q10:
How is speed converted from km/hour to m/second?
To convert km/hour to m/second, multiply by 5/18. To convert m/second to
km/hour, multiply by 18/5.
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Now that you have learned about units, measurement, measuring instruments, and physical quantities, it's time to test your knowledge.
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