In our daily lives, we constantly encounter situations where measurement is crucial, even if we don't always realize it. Measurement is the process of comparing an unknown quantity with some known, standard quantity. Every measurement consists of two parts: a number and a unit. But why is this so important?
Consider this common scenario: A boy asks his barber to cut his hair 'a little' off the forehead, without specifying an exact length. The barber, without a precise measurement, might cut off too much, leading to an unwanted haircut. Had the boy specified '2 cm' or '3 cm', the barber could have cut the hair exactly to his wish. This highlights how vague instructions without specific measurements can lead to undesired outcomes.
Similarly, in cooking, a recipe might say 'add a small amount of salt'. What is a 'small amount'? To one person, it might be 2 grams, to another, 5 grams. This lack of precision can significantly alter the taste of the dish. Professional chefs and bakers rely on exact measurements (e.g., 2 grams of salt, 150 ml of milk) to ensure consistency and quality in their culinary creations. [Illustration: Chef measuring ingredients precisely]
In construction and engineering, precision is even more critical. Imagine building a bridge where the length of a steel beam is 'about 10 meters' instead of exactly '10.00 meters'. Such approximations can lead to structural weaknesses, safety hazards, and catastrophic failures. Buildings, roads, and machines all require exact measurements for their components to fit together correctly and function safely. For example, as mentioned in our text, if the curvature of a key is changed even by 1 mm, the lock would not open. This shows the immense impact of even tiny inaccuracies in scientific and practical applications.
To perform tasks like measuring your height, drawing lines for a game like kabbadi, asking for potatoes from a shopkeeper, knowing how much milk your mother gets daily, or calculating travel time to school, we need to understand and apply measurement. The shopkeeper uses measuring tools to sell kerosene. All these daily activities, from the simplest to the most complex, rely on accurate measurement.
In this chapter, we will delve into the details of fundamental physical quantities like length, mass, and time, and explore the necessity and methods of measuring them precisely.
What is length? Length is defined as the distance between one point and another desired point. This could be the distance between the edges of your book, the corners of a football ground, or even the distance from your home to school.
The standard unit of length in the International System of Units (SI) is the 'metre', represented by the letter 'm'. For very small lengths, we use 'millimetre' (mm) and 'centimetre' (cm). Larger measures, like the height of a building, a banner, or a lamp post, are measured in metres. For even longer distances, such as between two cities or from your school to home, we use 'kilometre' (km).
Let's understand the units of length:
Think: Can you express 1 km in cm? (Answer: 1 km = 1000 m = 1000 × 100 cm = 100,000 cm)
Measuring length with a scale: To measure the length of an object like your pencil, take a metre scale. You'll notice lines marked 1, 2, 3... up to 15 or 30. The distance between two consecutive numbers (e.g., between 1 and 2) is one centimetre (cm). Within each centimetre, there are smaller markings. If you count, there are 9 such lines, making 10 divisions. The distance between any two consecutive smaller markings within a 'cm' denotes a millimetre (mm).
Mass is a fundamental physical quantity that measures the amount of matter in an object. The SI unit of mass is 'kilogram', represented by 'kg'.
It's important to distinguish between mass and weight. Weight is the gravitational pull experienced by matter. While mass is constant regardless of location, weight can change depending on the gravitational force. For example, on the Moon, where the gravitational force is less than on Earth, your weight would reduce, but your mass would remain the same. Objects weigh six times lighter on the Moon than on the Earth because the Moon's gravitational pull is one-sixth of the Earth's pull.
If you hold a sheet of paper in one hand and a book in the other, the hand holding the book feels heavier. This is because the mass of the book is greater than that of the paper, resulting in more gravitational pull on the book. The force we experience as 'heaviness' is weight.
Smaller masses are measured in grams (gm) and milligrams (mg). Bigger weights are measured in tonnes or metric tonnes.
Units of Mass:
We use instruments like beam balances and electronic balances to measure mass. A beam balance works by comparing the mass of an object to that of known standard masses. Electronic balances provide accurate measurements of mass, often correct up to milligrams. [Illustration: Beam balance and Electronic balance]
Time is the continuous sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. We observe the passage of time through changes like day turning into night, seasons changing, and our own growth.
The SI unit of time is 'second'.
How do we measure the change of time? Clocks are the most common tools used to measure time. You are familiar with reading time from a clock face. Historically, people used various methods to measure time. In earlier days, sand clocks and sundials were used, particularly during daylight hours. A sundial uses the shadow cast by a stick to estimate time, while a sand clock uses the flow of sand through a small hole to mark time intervals. For rough estimation, you can even use your pulse to count elapsed time. Today, we use more precise instruments like electronic clocks and stopwatches to measure even very small durations of time. [Illustration: Sundial and Sand clock]
Imagine if everyone used different units for measurement. In Activity 1, you might have noticed that when you and your friends measured height using non-standard units like hand spans or cubits, your measurements were different. This inconsistency makes it difficult to communicate measurements effectively.
Historically, different countries and regions used their own unique measuring units, leading to confusion and complications in trade and scientific exchange. To overcome this, scientists worldwide adopted a common set of units to express measurements. This standardized system is called the International System of Units, or SI Units.
The SI system ensures uniformity and accuracy in measurements across the globe, making scientific research, engineering, trade, and daily life much simpler and more reliable.
Here are the SI units for some fundamental quantities:
Multiples and Sub-multiples of SI Units are expressed using prefixes. These prefixes help us denote very large or very small quantities conveniently.
| Prefix | Abbreviation | Submultiple/Multiple | For Metre Example |
|---|---|---|---|
| Deci | d | Submultiple: 1/10 | 10 decimetre = 1 metre |
| Centi | c | Submultiple: 1/100 | 100 centimetre = 1 metre |
| Milli | m | Submultiple: 1/1000 | 1000 millimetre = 1 metre |
| Nano | n | Submultiple: 1/1,000,000,000 | 1,000,000,000 nanometre = 1 metre |
| Kilo | k | Multiple: 1000 | 1000 metre = 1 kilometre |
Measurement needs to be accurate, and the approach used must always be correct. While small approximations might not significantly impact daily life, they can have a large impact in scientific calculations and precise applications like engineering or medicine. Therefore, understanding common errors and how to avoid them is vital.
Common mistakes while using a scale:
Form a group of 5 members. Select one person and let others measure her/his height individually using their hand span and cubit. Compare your answers with others. Do you find any difference? Why? Now, all stand in front of a wall and mark your height on the wall. Measure your height with a scale. What differences do you infer?
Outcome: This activity demonstrates the inconsistency and lack of uniformity when using non-standard units of measurement, highlighting the need for standard units like the metre.
Materials needed: A metre scale, a measuring tape, a string, and a sketch pen
Method:
This distance will give you the length of the curved line. Try to find the length of a banana using this method.
Materials needed: A divider, a ruler, paper, pencil
Method:
Construct your own beam balance using two scrapped coconut shells, strings or twines, thick cardboard as a frame, and a sharpened pencil as an index needle. What can you achieve? Find which object is heavier. Find the approximate weight of lighter things like leaves, pieces of paper, etc.
Outcome: This activity helps in understanding the principle of a beam balance and relative weights of objects.
Ask four or five of your friends to run a race from one end of the school to the other end. Mark the starting point and the ending point. Using your pulse (or by counting '1, 2, 3...') count the time taken by each of them to complete the race. Check who is fast?
Outcome: This activity provides a practical, albeit rough, method for understanding and measuring time intervals.
1. What is the primary reason why SI units were adopted globally?
Answer: SI units were adopted globally to ensure uniformity and accuracy in measurements, facilitating easier communication, trade, and scientific collaboration worldwide.
2. Explain how a tiny error in measurement can have significant consequences in a practical application like building a house.
Answer: In building a house, even a small error in measurement, like a beam being off by a few centimetres, can lead to structural instability, doors and windows not fitting properly, or even collapse. Precise measurements ensure safety, durability, and functionality of the structure.
3. Describe two historical methods people used to measure time before modern clocks were invented.
Answer: Two historical methods for measuring time include the sundial, which uses the changing position of a shadow cast by a stick to indicate time, and the sand clock (or hourglass), which measures time based on the fixed rate at which sand flows from one bulb to another through a narrow opening.
1. How many millimetre divisions are there in a centimetre? Answer: 10
2. How many centimetre divisions are there in a metre? Answer: 100
a) 7875 cm = 78 m 75 cm
b) 1195 m = 1 km 195 m
c) 15 cm 10 mm = 160 mm
d) 45 km 33 m = 45033 m.
The height of a tree can be measured by
Answer: measuring tape
Conversion of 7 m into cm gives
Answer: 700 cm
Quantity that can be measured is called
Answer: physical quantity
While measuring the length of an object using a ruler, the position of your eye should be
Answer: vertically above the point where the measurement is to be taken
Which of the following is NOT an SI unit?
Answer: foot
The standard unit of mass is
Answer: kilogram
What does an odometer measure?
Answer: distance travelled
Which of these errors occurs when the eye is not positioned correctly while taking a reading?
Answer: parallax error
1 kilometre is equal to how many metres?
Answer: 1000 m
A beam balance is used to measure
Answer: mass
The historical instrument used to measure time during the day by shadow is a
Answer: sundial
Which of the following describes the amount of matter in an object?
Answer: mass
If you are asked to cut a piece of string exactly 15.5 cm long, what tool would be most appropriate?
Answer: measuring tape with cm and mm markings
Which prefix represents 1/1000 of the basic unit?
Answer: milli
The force experienced as 'heaviness' is called
Answer: weight
Which of these is a multiple of the metre?
Answer: kilometre
What is the SI unit of time?
Answer: second
To measure the length of a curved line accurately, you can use a string and then measure the string with a
Answer: all of the above
If a balance shows a reading even when nothing is placed on it, it indicates a
Answer: zero error
The metric system was created by which country?
Answer: France
1 metre is equal to how many millimetres?
Answer: 1000 mm
Why is precise measurement crucial in engineering?
Answer: To ensure components fit and function safely
Which of the following is NOT a fundamental physical quantity discussed?
Answer: temperature
The SI unit of length is represented by
Answer: m
What is the effect of moving an object from Earth to the Moon on its mass and weight?
Answer: Mass remains same, weight decreases
Which instrument provides accurate measurement of mass correct up to milligram?
Answer: electronic balance
What is the abbreviation for centimetre?
Answer: cm
How many grams are in 1 kilogram?
Answer: 1000 gm
The distance between two points is called
Answer: length
Which historical unit of length was based on the length from the elbow to the tip of the middle finger?
Answer: cubit
What is the purpose of prefixes in SI units?
Answer: To denote very large or very small quantities
An example of a situation where vague measurement can lead to a negative outcome is
Answer: asking a barber to cut hair 'a little'
Which unit is used for measuring distances between celestial bodies?
Answer: light-year
The '0' mark on a scale should coincide with the object's starting point to avoid
Answer: zero error
How many millimetres make one centimetre?
Answer: 10 millimetre
If you measure your height using your hand span and then with a measuring tape, you will likely find differences because
Answer: hand span is a non-standard unit
What is the standard unit of length?
Answer: metre
Which of these is a sub-multiple of the metre?
Answer: millimetre
The comparison of an unknown quantity with some known quantity is called
Answer: measurement
Which of the following is a physical quantity?
Answer: length
The SI unit of area is
Answer: square metre
1 tonne is equal to how many kilograms?
Answer: 1000 kilogram
If a recipe calls for 'a small amount of salt' and you add '2 grams', you are practicing
Answer: precision
Which of these devices is used to measure time?
Answer: stopwatch
The process of making measurements easier and more reliable globally led to the adoption of
Answer: SI units
The SI unit of volume is
Answer: cubic metre
Which of the following conversions is correct?
Answer: 1 cm = 10 mm
If an object is tilted while measuring its length with a scale, the reading will be
Answer: less accurate
What is the primary characteristic of a 'physical quantity'?
Answer: It can be measured
A standard metre rod and kilogram bar are kept in which city?
Answer: Paris
What is the standard unit of time in the International System of Units?
Answer: Second
Which of the following is true about mass and weight?
Answer: Weight changes with gravity, mass does not.
What is the primary reason for adopting SI units globally?
Answer: To ensure uniformity and avoid confusion in measurements.
Which prefix indicates a multiple of 1000?
Answer: Kilo
If you are measuring the length of a table, which unit would be most appropriate?
Answer: Metre
Which instrument is best for precise measurement of small lengths like a pencil tip?
Answer: Ruler with millimetre markings
What is the term for a common mistake where the '0' mark of the measuring instrument does not align with the actual zero point?
Answer: Zero error
Which of these activities demonstrates the need for standard units?
Answer: Measuring height using hand span and comparing with others.
How many parts does a measurement of a quantity typically have?
Answer: Two
What is the second part of a measurement, besides the number?
Answer: Unit
Which instrument would be best for finding the accurate measurements of weight in a laboratory?
Answer: Electronic balance
The distance travelled by light in one year is known as a
Answer: light-year
| Item | Match |
|---|---|
| Length of the fore arm | Cubit |
| SI unit of length | Metre |
| Nano | 10⁻⁹ |
| SI Unit of time | Second |
| Kilo | 10³ |
1 Metre, 1 centimetre, 1 kilometre, and 1 millimetre.
Answer: 1 millimetre < 1 centimetre < 1 metre < 1 kilometre
kilogram, millimetre, centimetre, nanometre
Answer: Kilogram (It is a unit of mass, while others are units of length)
Find the answer for the following questions within the grid (Grid not provided, so answers are given):
| Property | Definition | Basic Unit | Instrument used for measuring |
|---|---|---|---|
| Length | |||
| Mass | |||
| Volume | |||
| Time |
Solution for the chart:
| Property | Definition | Basic Unit | Instrument used for measuring |
|---|---|---|---|
| Length | Distance between two points | metre (m) | Ruler, Measuring tape, Metre scale |
| Mass | Amount of matter in an object | kilogram (kg) | Beam balance, Electronic balance |
| Volume | Amount of space occupied by an object | cubic metre (m³) | Measuring cylinder, Graduated beaker |
| Time | Duration of an event | second (s) | Clock, Stopwatch, Sundial (historical) |
Test your knowledge with this quick quiz!