Deepa, a curious eleven-year old girl, lives in a town of the state of Haryana. The new school year has started. Deepa needs a new uniform since she has grown taller. Her mother takes her to a cloth shop. She asks for a two-metre cloth piece. The shopkeeper measures the cloth using a metal measuring rod.
Then, the tailor takes her measurements using a flexible measuring tape. Her mother instructs the tailor to increase the length of her uniform by char angula (four fingers width).
Are the tape and rod similar to the scale that the elder sister has in her geometry box? What did mother mean by char angula?
Deepa shares her experience with her school friends Anish, Hardeep, Padma, Tasneem and this leads to a discussion amongst them.
Table 5.1: Measuring the length of the table
| Name of the Student | Number of Handspans |
|---|---|
| Anish | Slightly more than 13 |
| Padma | 13 |
| Tasneem | Slightly less than 13 |
| Deepa | Between 13 and 14 |
| Hardeep | 14 |
However, handspans and other similar units, such as length of hand, foot, fist or fingers, differ from person to person. Thus, there is a need for such a unit for which measurements of the same length made by different people do not differ.
Several systems of units evolved with time in different parts of the world. However, when people started travelling from one place to another, it created a lot of confusion. This led to the different countries coming together and adopting a set of standard units of measurement. The system of units now used is known as the "International System of Units" or SI units.
Look carefully at the 15-cm scale. It has markings (in cm) from 0 to 15. The length of any section between two consecutive big marks, such as between 1 and 2 or between 5 and 6, is 1 cm. Observe that these sections of 1 cm length are further divided into 10 equal parts. The length of one of these smaller parts is called a millimetre (mm). 1 mm is the smallest value of length that you can measure using this scale. 1 mm is equal to one-tenth of a centimeter (1 mm = 0.1 cm).
Conversion of Units
| Conversion |
|---|
| 1 km = 1000 m |
| 1 m = 100 cm |
| 1 cm = 10 mm |
Would it be convenient to use the unit metre to measure larger lengths, such as the length of a railway track between two cities, or to measure smaller lengths, such as the thickness of a page of a book?
For measuring any length, we need an appropriate scale. For example, if you want to measure the length of your pencil, you may use a 15-cm scale. Similarly, if the height of a room is to be measured, you may need a metre scale or a measuring tape. You cannot directly measure the girth of a tree or the size of your chest using a metre scale. For such measurements, flexible measuring tape, such as a tailor's tape is more suitable.
While measuring lengths, we need to take care of some points.
- •Select some objects around you, such as a comb, a pen, a pencil, and an eraser to measure their lengths.
- •Measure their lengths one by one using a metre scale and note down the measurements in Table 5.2.
Table 5.2: Measuring lengths
| Object | Length of the object |
|---|---|
Place the scale in contact with the object along its length.
For example, if you are trying to measure the length of a pencil by aligning it with a scale, the position of your eye should be directly above the tip of the pencil.
If the ends of the scale are broken or the zero marking is not clear, it can still be used for measurement. With such a scale, use any other full mark of the scale, say, 1.0 cm. Then you must subtract the reading of this mark from the reading at the other end. For example, if the reading at one end is 1.0 cm and at the other end, it is 10.4 cm, then the length of the object is 10.4 cm - 1.0 cm = 9.4 cm.
While writing the length, do not forget to write the unit also. Thus, your result will consist of two parts—one part is a number and the other part is the unit of measurement.
Some of your friends in the class would have measured the length of the same objects. Compare the lengths measured by you with that of your friends. Are the measured lengths the same or slightly different? If not the same, discuss the possible reasons for the differences.
Anish and his parents fixed electric string lights on the arches of the verandah of their house for a celebration at home. How would they have measured the required length of string lights?
In the case of a curved line, measurements can be made with the help of a flexible measuring tape or by using a thread. The thread can then be straightened and its length can be measured using a metre scale.
One day the teacher informs her students that she has planned an educational visit to a nearby garden. She asks the students to reach there directly in the morning. Deepa and her friends start discussing whether the garden would be closer than their school or farther. Tasneem and Padma say that the garden would be closer, while Deepa and Anish feel that the school would be closer. Hardeep thinks that both would be almost at an equal distance.
Who do you think is correct? All of them are correct. Then, why are their observations different? They are locating the distances of the school and garden from their houses.
A few days later, Hardeep tells his friends excitedly, "Let us all go to the playground. The sports teacher wants us to help her to draw lines with chuna powder (limestone powder) for making the Kabaddi court for the sports day."
After a few days, Padma was travelling by bus to visit her grandparents in Delhi. She was eager to reach Delhi and was reading the kilometre stones on the side of the road. On one of the kilometre stones, it was written "Delhi 70 km". Further on, the next kilometre stone read "Delhi 60 km". Each kilometre stone indicated to her that she was getting closer to her grandparents' house.
If the kilometre stone reads "Delhi 70 km", we can say that the position of Padma is 70 km from Delhi. When the kilometre stone reads "Delhi 60 km", the position of Padma is at 60 km from Delhi.
Does this mean that the position of Padma, with respect to the reference point, is changing with time? When does the position of an object change with respect to a reference point? Does it change when an object is moving?
- •Look around and prepare a list of five objects that are in motion and five objects that are at rest.
- •Record your observations in Table 5.3.
- •Think about how you decided whether an object was in motion or at rest. Write your explanation (justification) in Table 5.3.
Table 5.3: Observing things around you
| Objects in motion | Justification | Objects at rest | Justification |
|---|---|---|---|
| Cow grazing in the field | Tree | ||
Compare and analyse your justifications. How can one decide if an object is in motion or at rest?
Deepa looked around her in the bus and noticed that all the passengers were seated. She looked around again after a minute and found them still occupying their seats. She wondered, "Are they moving?" She concluded that the position of the passengers was not changing with time. Therefore, they were certainly at rest. However, when she looked outside, she felt they were in motion as their positions were changing with respect to things outside.
- •Take an eraser and drop it from a certain height.
- •Observe its motion.
Does it move along a straight line? When an orange drops from the tree, does it move in a straight line? Have you seen the Republic Day parade? Recall the march-past of students during the parade. Do they move on a straight-line path? When a heavy box is pushed, it may also move along a straight line.
Identify such linear motion in your surroundings. But do things always move along a straight line? You might have enjoyed playing on swings and merry-go-rounds. Are these types of motion also linear motion?
- •Tie an eraser (or a potato) at one end of a thread.
- •Hold the other end of the thread with your hand and whirl it.
- •Observe its motion.
Is the motion of the eraser the same as that of a merry-go-round?
- •Tie an eraser (or a potato) at one end of a thread.
- •Hang the eraser by holding the other end of the thread. Keep your hand steady.
- •Using the other hand, take the eraser slightly to one side and then release.
Does it start moving to and fro? Is its motion similar to the motion of a swing?
- •Take a thin metal strip of about 50 cm long.
- •Hold its one end pressed to a table. You may use a few books or a brick to hold it.
- •Press the free end of the strip slightly and let it go.
- •Observe the motion of this end of the strip.
Does it move up and down? This is also an example of oscillatory motion.
- •Look at the picture of a children's park or visit a children's park.
- •Observe different kinds of motions. <strong>Classify</strong> them as linear, circular or oscillatory motion.
- •List them in Table 5.4. Give your justification for why you put each in a certain category.
Table 5.4: Types of Motion
| Object | Linear motion | Circular motion | Oscillatory motion |
|---|---|---|---|
| Swing | Moving to and fro | ||
Keywords
- 1The International System of Units (SI units) has been adopted by countries as standard units of measurement.
- 2The SI unit of length is metre. Its symbol is m.
- 31 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
- 4When distance is stated with respect to a fixed object or point, then this point is called a reference point.
- 5An object is said to be in motion if its position changes with respect to a reference point with time.
- 6When an object moves along a straight line, its motion is called linear motion.
- 7When an object moves along a circular path, its motion is called circular motion.
- 8When any object moves to and fro about any fixed position, its motion is called oscillatory motion.
- Can you find the thickness of a single page of your notebook or textbook using a scale? Think of a way and write it. Carry out the activity and report your result.
- Collect fallen leaves from the same tree. Identify the name of the tree whose leaves you have taken. Measure length and breadth of all these leaves using a 15-cm scale. Record your observations and discuss why the leaves of the same tree vary in length and breadth.
- Discuss with elders in your community what units were used for measurement of length in the olden days. Also, using the internet, try to find out about the length scales found in excavations of archaeological sites in India.
- Create a maze using lines of 1 cm, 2 cm and their combination. Use your imagination and expand it to a size as big as you want.
- How tall am I? Stand along a wall and with the help of an adult, mark your height. Repeat it every three months to maintain a height record for yourself and your siblings.
- Let us design a fun method for measuring the distance between two places by using a bicycle. Attach a flexible metal strip to the spoke of the front wheel. Count the number of times the sound occurs. This number gives the number of turns of your wheel. Measure the length of the outer boundary of the wheel using a string. Multiply this length by the number of turns. This is the distance you travelled. Try to find out about a "Jones Counter" which is attached to a bicycle wheel and is used for measuring distances.
