Chapter: 02. Physical Quantities And Measurement 1
Physical Quantities and Measurement - 1
What You Will Learn in This Chapter:
Define Length and Mass: Understand what these fundamental quantities are. Express Length and Mass in Proper Units: Learn to use the correct units and symbols for length and mass. Measure Length: Discover how to use instruments like a ruler and a measuring tape to find the length of objects. Measure Mass: Understand how to use a beam balance and an electronic balance to determine the mass of an object. Measure Area: Learn to measure the area of regular objects using a graph paper. Convert Units: Practice converting physical quantities from one unit to another related unit. Connecting to Your World
In our daily lives, we often encounter situations where measurement is essential. Think about going to a shop: shopkeepers use specific instruments to measure things you want to buy.
For example, to get flour, sugar, or vegetables, a scale is used to measure their weight (which in physics, we call mass). To get a length of cloth or to measure a table, a measuring tape is used.
Introduction to Measurement
Measurement is a crucial part of our daily activities, whether we are at home, in a shop, or at a doctor’s clinic.
Measuring Length: To find the distance from your house to your school, or how much cloth is needed for a dress, you measure length. Measuring Mass: When buying items like fruits, vegetables, salt, or wheat, the shopkeeper measures their quantity, which involves the measurement of mass. Measuring Volume: The amount of petrol for a car or milk for home involves measuring volume. What is a Physical Quantity?
A physical quantity is anything that can be measured.
What is Measurement?
Measurement is the process of comparing an unknown quantity with a known, fixed quantity of the same kind. The known fixed quantity used for comparison is called a unit.
Parts of a Measurement Value:
Every measurement value has two essential parts:
Numerical Value: A number (e.g., 103). Unit of Measurement: The specific unit used (e.g., kilometres). For example, if a road sign indicates “Kozhikode 103 kilometres” (Fig. 2.1), 103 is the numerical value, and kilometre is the unit.
Without both these parts, a measurement is incomplete or incorrect.
SI Units
Historically, people used body parts like hand span or foot to measure length. However, these measurements varied from person to person, leading to inconsistencies. To solve this, a worldwide standard system of measurement, known as the metric system or International System of Units (SI units), was introduced.
Standard SI Units:
Therefore, when a distance is 103 kilometres, it means it is 103 times the standard length of 1 kilometre.
Measurement of Length
Definition of Length (Sci-Vocab):
Length is defined as the distance between any two points or places. When you measure width, height, depth, thickness, radius, or circumference of any object, you are essentially measuring length.
Units of Length
The standard unit of length in the SI system is the metre (m).
Metre (m): A convenient unit for measuring things like the length of cloth or a table. Kilometre (km): A bigger unit needed for measuring long distances, such as between two towns or from home to school. Centimetre (cm) and Millimetre (mm): Smaller units used for measuring shorter lengths, like a pencil or a notebook. Commonly Used Units of Length:
Common Relations Between Units of Length: Multiples and Submultiples:
Kilometre is a multiple of the standard unit metre (meaning it’s larger). Centimetre and millimetre are submultiples of the standard unit metre (meaning they are smaller). Unit Conversions (How to Convert):
To convert millimetre (mm) into centimetre (cm), divide the number of mm by 10. To convert centimetres (cm) into metres (m), divide the number of cm by 100. To convert kilometre (km) into metres (m), multiply the number of km by 1000. Solved Numerical Examples for Length Conversion:
a. 10 m to cm:
Since 1 m = 100 cm,
10 m = 10 × 100 cm = 1000 cm b. 7500 m to km:
Since 1000 m = 1 km,
7500 m = 7500 / 1000 km = 7.5 km c. 500 cm to mm:
Since 1 cm = 10 mm,
500 cm = 500 × 10 mm = 5000 mm d. 300 cm to m:
Since 100 cm = 1 m,
300 cm = 300 / 100 m = 3 m Find the thickness of a 2-rupee coin if a stack of height 4 cm is made by placing ten 2-rupee coins one upon the other. Height of the stack = Thickness of ten 2-rupee coins = 4 cm Convert stack height to mm: 4 cm = 4 × 10 mm = 40 mm Thickness of one 2-rupee coin = (40 mm) / 10 coins = 4 mm
Instruments Used to Measure Length
The most common instruments for measuring length are the ruler, metre scale, and measuring tape (Fig. 2.2).
Metre Scale: Used by cloth merchants to measure cloth length. It has 100 divisions, each equal to 1 centimetre. Each centimetre has 10 small divisions, each equal to 1 millimetre. Measuring Tape: Used by tailors, carpenters, and building constructors. Tapes can be 1 m to 100 m long and have markings in millimetres, centimetres, and metres. Ruler: Similar to a metre scale but smaller, used for measuring shorter lengths. Rulers often have both centimetre and inch markings (Fig. 2.3). One inch is approximately 2.5 cm.
Observation of a Ruler:
When observing a ruler from a geometry box, you will notice:
A specific number of centimetres marked. That 1 centimetre is divided into 10 millimetres. A specific number of inches marked. That approximately 25.4 millimetres are equal to 1 inch (since 1 inch = 2.54 cm and 1 cm = 10 mm). Reason Corner (Think About This):
A measuring tape is not used to measure the distance from Delhi to Chennai because such long distances are best measured in kilometres, and a measuring tape, even a 100-meter one, is impractical for such vast distances.
Activity: Measuring the Length of a Wooden Block
Aim: To measure the length of a wooden block. Materials: A ruler or a metre scale and a wooden block. Place the ruler or metre scale exactly along the length of the block. Ensure the zero mark of the ruler aligns with one end of the block. Read the measurement at the other end of the block (Fig. 2.4). If the end falls between two markings (e.g., 3.1 cm and 3.2 cm), take the reading closer to the end for an approximate length. Observation: In the example (Fig. 2.4), the length of the wooden block would be observed as 5 cm. Conclusion: The reading obtained is the length of the given wooden block.
Precautions While Taking Measurements
To ensure accurate length measurements, keep the following precautions in mind:
Always place the object to be measured on a flat, even surface. An uneven surface will lead to incorrect measurements. Placement of the Ruler or Metre Scale: Place the measuring instrument exactly along the length of the object. Do not keep the ruler at an angle to the length, as this will result in inaccurate measurement (Fig. 2.5 illustrates incorrect angles). Keep the ruler as close as possible to the object. Ensure the zero mark of the ruler is placed precisely at the beginning end of the object. Position of the Eye (Parallax Error): Sci-Vocab: Parallax Error: The error that occurs due to incorrect positioning of the eye during measurement. Keep your eye vertically above the point from where you are taking the measurement (Position B in Fig. 2.6). Viewing from an angle (Positions A or C in Fig. 2.6) will give wrong results due to parallax error. To avoid parallax error, it is advised to keep one eye shut while taking the measurement.
Condition of the Ruler (Broken or Worn Edges): If the ruler is broken, has worn-out edges, or the zero mark is not clearly visible: Start measuring from a clear mark, such as 1 cm or 2 cm. After taking the reading at the other end of the object, subtract the starting mark’s value from the final reading. Example: If you start at the 2 cm mark and the other end is at 7 cm (Fig. 2.7), the length of the object is (7 - 2) cm = 5 cm.
Life Skills (Thinking and Collaboration):
Working in groups to find and measure different lengths in the classroom (e.g., distance between desks, length of the classroom/door/book) is a good way to practice these skills and present data in an organized manner.
Measurement of Mass
You might notice that a jug filled with milk feels heavier than a glass filled with milk (Fig. 2.8). This is because the jug contains a larger quantity of matter (milk) than the glass.
The quantity of matter in a body determines its mass. So, the milk in the jug has more mass than the milk in the glass. Similarly, a bucket with water has more mass than an empty bucket. Mass vs. Weight (Myth vs Fact):
Myth: Mass and weight are the same. Mass: The quantity of matter contained in a body. Weight: The force of gravity exerted on the body due to its mass. A person can be weightless if there is no gravity, but they cannot be without mass.
In everyday language, we often say “weight” (e.g., a bag of vegetables weighs 6 kg), but scientifically, the correct term is “the mass of the bag of vegetables is 6 kg.” Units of Mass
The standard unit of mass in the SI system is the kilogram (kg).
Commonly Used Units of Mass:
Common Relations Between Units of Mass: Multiples and Submultiples:
Quintal and metric ton are multiples of kilogram, used for measuring the mass of heavier bodies. Grams and milligrams are submultiples of kilogram, used for measuring the mass of lighter bodies. Science Alive (National Standards):
The National Physical Laboratory (NPL) in New Delhi is responsible for maintaining the national standards for all basic units in India. The standard metre and standard kilogram are kept at the NPL.
Solved Numerical Example for Mass Conversion:
John bought 5 packets of biscuits, each containing 20 biscuits. The total mass of the biscuits was 2.5 kg. What was the mass of each biscuit in grams? Total number of biscuits in 5 packets = 5 packets × 20 biscuits/packet = 100 biscuits Total mass of 100 biscuits = 2.5 kg Convert total mass to grams: 2.5 kg = 2.5 × 1000 g = 2500 g Mass of 1 biscuit = 2500 g / 100 biscuits = 25 g Thus, the mass of each biscuit is 25 g. Key Facts on Mass Measurement:
The standard unit of mass in the SI system is the kilogram. Instruments Used to Measure Mass
Mass is typically measured using various types of balances. The most common are the beam balance and the electronic balance.
Structure: Has a horizontal beam supported at its centre by a metal loop (acting as a lever). A pointer is fixed at the centre. Two identical pans of equal weight hang on either side of the beam, equidistant from the centre. Ensure the beam is horizontal when pans are empty. Place the object to be weighed in one pan. Place standard weights in the other pan until the beam becomes horizontal. The vertical position of the pointer indicates balance. The total sum of the standard weights placed gives the mass of the object.
Electronic Balance (Fig. 2.10): Structure: Has a platform where the object is placed. Measurement Process: Provides a direct digital display of the object’s mass. Characteristics: Very accurate and sensitive.
Precautions While Taking Mass Measurements
When buying goods from the market, it’s important to be aware of the following to ensure fair measurement:
Checking Beam Balance and Weights: 
Self Study
Without both these parts, a measurement is incomplete or incorrect.
Common Relations Between Units of Length:
The quantity of matter in a body determines its mass. So, the milk in the jug has more mass than the milk in the glass. Similarly, a bucket with water has more mass than an empty bucket.
Common Relations Between Units of Mass:
