1.0 Introduction to Measurement
In Physics, we study the natural world through observations and experiments. To make these observations accurate, we need Measurement. Measurement is the process of comparing an unknown quantity with a known fixed quantity of the same kind.
Physical Quantities
Any quantity that can be measured is called a Physical Quantity. Examples include length, mass, time, temperature, and area.
Components of Measurement
Every measurement consists of two parts:
- The Number (Magnitude): Tells us how many times the unit is contained in the quantity.
- The Unit: A fixed standard used for comparison.
Measurement Expression
$$Physical\,Quantity = n \times u$$
Where: $n$ = numerical value, $u$ = unit
1.1 Systems of Units
To maintain uniformity across the world, scientists developed the International System of Units (SI Units). Earlier, different systems like CGS (Centimetre-Gram-Second) and FPS (Foot-Pound-Second) were used.
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Length | Metre | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Temperature | Kelvin | K |
Identify the numerical value and the unit in the measurement: "The length of a table is 1.5 metres."
Solution:
1. Numerical value ($n$) = 1.5
2. Unit ($u$) = metre (m)
Measurement = $n \times u = 1.5\,m$
Symbols of units are never written in plural form. For example, we write 10 kg, not 10 kgs. Also, a full stop is not placed after the symbol unless it is at the end of a sentence.
2.0 Measurement of Length
Length is defined as the distance between any two points. In our daily lives, we measure length for various purposes, such as measuring the height of a person, the length of a cloth, or the distance between two cities.
Standard Unit of Length
The SI unit of length is the metre (m). For very large distances, we use kilometres (km), and for smaller lengths, we use centimetres (cm) or millimetres (mm).
Common Instruments for Measuring Length
- Metre Scale: Used for measuring short lengths (up to 1 metre).
- Measuring Tape: Used for measuring longer distances or curved surfaces (like the waist of a person).
- Vernier Callipers: Used for measuring the diameter of small spherical or cylindrical objects (Advanced tool).
Length Unit Conversions
$$1\,km = 1000\,m$$ $$1\,m = 100\,cm$$ $$1\,cm = 10\,mm$$
To convert larger units to smaller, multiply; to convert smaller to larger, divide.
1. Zero Mark: Place the object exactly at the '0' mark of the scale.
2. Parallax Error: Keep your eye vertically above the point where the measurement is to be taken to avoid wrong readings.
The distance between two pillars is 4500 metres. Convert this distance into kilometres.
Solution:
1. Given: Distance = $4500\,m$
2. We know: $1\,km = 1000\,m$
3. Conversion: To convert $m$ to $km$, we divide by 1000.
4. Calculation: $$\frac{4500}{1000} = 4.5\,km$$
Result: The distance is $4.5\,km$.
3.0 Measurement of Mass
Mass is the quantity of matter contained in a body. Unlike weight, the mass of an object remains constant everywhere in the universe, whether you are on Earth, the Moon, or in deep space.
Standard Unit of Mass
The SI unit of mass is the kilogram (kg).
• For smaller masses, we use grams (g) or milligrams (mg).
• For very large masses (like a truckload of grain), we use quintals or metric tonnes.
Common Instruments for Measuring Mass
To measure mass, we compare an unknown mass with known standard masses using:
- Beam Balance: A simple lever with two pans.
- Physical Balance: A highly sensitive version of the beam balance used in laboratories.
- Electronic Balance: A modern device that gives very accurate digital readings.
Mass Unit Conversions
$$1\,kg = 1000\,g$$ $$1\,g = 1000\,mg$$ $$1\,tonne = 1000\,kg$$
Note: 1 Quintal = 100 kg
A bag contains 2.5 kg of sugar. How many grams of sugar are in the bag?
Solution:
1. Given: Mass in kg = $2.5\,kg$
2. We know: $1\,kg = 1000\,g$
3. Conversion: To convert $kg$ to $g$, multiply by 1000.
4. Calculation: $$2.5 \times 1000 = 2500\,g$$
Result: The bag contains $2500\,g$ of sugar.
In common language, we use "mass" and "weight" interchangeably, but in Physics, they are different. Weight is a force (measured in Newtons) that changes with gravity, while Mass is constant!
4.0 Measurement of Time
Time is the interval between two events. Since ancient times, humans have measured time using periodic phenomena like the rising and setting of the sun, or the phases of the moon. In modern physics, we require much more precise measurements.
Standard Unit of Time
The SI unit of time is the second (s).
• Larger units include minutes (min), hours (h), days, months, and years.
• 1 Mean Solar Day is the time taken by the Earth to complete one rotation on its axis.
Instruments for Measuring Time
- Pendulum Clock: Based on the periodic swing of a pendulum.
- Watch/Clock: Modern quartz clocks use the vibrations of quartz crystals.
- Stopwatch: Used to measure specific intervals of time in sports or laboratory experiments. It can be started or stopped at will.
Time Unit Conversions
$$1\,minute = 60\,seconds$$ $$1\,hour = 60\,minutes = 3600\,seconds$$ $$1\,day = 24\,hours$$
How many seconds are there in 2 hours and 15 minutes?
Solution:
1. Convert hours to seconds: $$2 \times 3600 = 7200\,s$$
2. Convert minutes to seconds: $$15 \times 60 = 900\,s$$
3. Total time in seconds: $$7200 + 900 = 8100\,s$$
Result: There are $8100\,seconds$.
A Sundial was one of the earliest time-keeping devices. It uses the position of the shadow cast by the sun to tell the time of day!
5.0 Measurement of Temperature
Temperature is a physical quantity that expresses the degree of hotness or coldness of an object. When we touch an object, our sense of touch tells us if it is hot or cold, but to know how hot or cold it is, we need a reliable measurement.
Standard Unit of Temperature
The SI unit of temperature is the Kelvin (K). However, in our daily lives and in the laboratory, we commonly use the degree Celsius (°C) or degree Fahrenheit (°F).
The Thermometer
A Thermometer is the device used to measure temperature. Most thermometers use Mercury because it remains in liquid state over a wide range of temperatures and expands uniformly when heated.
- Clinical Thermometer: Used to measure human body temperature ($35^\circ C$ to $42^\circ C$).
- Laboratory Thermometer: Used for scientific experiments (usually $-10^\circ C$ to $110^\circ C$).
Temperature Conversion Formulas
$$\frac{C}{5} = \frac{F - 32}{9}$$ $$K = C + 273$$
Where: $C$ = Celsius, $F$ = Fahrenheit, $K$ = Kelvin
The normal body temperature of a healthy human is $37^\circ C$. Convert this into Fahrenheit (°F).
Solution:
1. Given: $C = 37$
2. Formula: $\frac{C}{5} = \frac{F - 32}{9}$
3. Substitution: $\frac{37}{5} = \frac{F - 32}{9}$
4. Calculation: $7.4 \times 9 = F - 32 \implies 66.6 + 32 = F$
Result: $F = 98.6^\circ F$
Never wash a clinical thermometer with boiling water! The high temperature can cause the mercury to expand too much and break the glass tube.
6.0 Measurement of Area and Volume
While length, mass, and time are fundamental quantities, Area and Volume are derived from length. They help us understand how much surface an object covers and how much space it occupies.
6.1 Area
The total surface covered by a closed figure is called its Area. The SI unit of area is the square metre ($m^2$).
Area Formulas
Rectangle: $Area = length \times breadth$
Square: $Area = side \times side$
6.2 Volume
The space occupied by a three-dimensional object is called its Volume. The SI unit of volume is the cubic metre ($m^3$). For liquids, we commonly use Litres (L).
Volume Formulas
Cube: $Volume = side \times side \times side$
Cuboid: $Volume = l \times b \times h$
Note: $1\,L = 1000\,cm^3 = 1000\,mL$
Measuring Irregular Solids
To find the volume of an irregular solid (like a stone), we use the Water Displacement Method with a measuring cylinder.
A measuring cylinder is filled with water to the 50 mL mark. When a stone is immersed, the water level rises to 75 mL. What is the volume of the stone?
Solution:
1. Initial Volume ($V_1$) = $50\,mL$
2. Final Volume ($V_2$) = $75\,mL$
3. Volume of Stone = $V_2 - V_1$
4. Calculation: $75 - 50 = 25\,mL$
Result: Since $1\,mL = 1\,cm^3$, the volume of the stone is $25\,cm^3$.
When reading the level of water in a glass cylinder, always look at the lower meniscus (the bottom of the curve) at eye level to get an accurate reading.