Chapter 5: Measurement of Length and Motion

 Chapter 5: Measurement of Length and Motion

1. Measurement of Length:-Measurement means finding the size or amount of something by comparing it with a standard unit.

In earlier times, people used body parts such as:

• Handspan (balisht)
• Finger width
• Foot
• Arm length
• Stride

However, these measurements are not reliable because body parts differ in size from person to person. Therefore, standard units are needed.     

2. Unit of Measurement:-A measurement has two parts:

1. A number

2. A unit

For example, 13 cm means 13 is the number and centimetre (cm) is the unit.     

3. Standard Units:-The internationally accepted system of units is called the International System of Units (SI).

The SI unit of length is metre (m).     

Important units of length

Unit Symbol Relation

Kilometre km 1 km = 1000 m

Metre m 1 m = 100 cm

Centimetre cm 1 cm = 10 mm

Millimetre mm 1 mm = 0.1 cm

Thus:

1 km = 1000 m

1 m = 100 cm

1 cm = 10 mm     

Which unit should we use?

- Distance between two cities → kilometre

- Length of a classroom → metre

- Length of a pencil → centimetre

- Thickness of a page → millimetre

4. Measuring Instruments

Different objects require different measuring instruments.

- 15-cm scale → pencil, eraser, small objects

- Metre scale → larger objects

- Measuring tape → height, room dimensions

- Flexible tape → curved objects, chest or tree girth

A flexible measuring tape is useful when the object is curved.     

5. Correct Way of Measuring Length

While measuring:

1. Place the scale along the length of the object.

2. The scale should be in proper contact with the object.

3. Keep your eye directly above the end of the object while taking the reading.

4. Always write the number and unit together.     

If the zero mark is damaged

A broken scale can still be used.

For example:

- Starting reading = 1.0 cm

- Ending reading = 10.4 cm

Length = 10.4 − 1.0

= 9.4 cm     Chapter 5 Measurement of Length…

6. Measuring a Curved Line:- A curved line cannot always be measured directly with a straight scale.

Two methods can be used:

Method 1: Flexible measuring tape

Place the tape along the curve and read its length.

Method 2: Thread

1. Place a thread along the curved line.

2. Mark the ends.

3. Straighten the thread.

4. Measure the thread using a scale.     Chapter 5 Measurement of Length…

7. Reference Point:-A reference point is a fixed object or point with respect to which the distance or position of another object is described.

For example, if we describe a person's position as 70 km from Delhi, then Delhi is the reference point.    Example

If a kilometre stone says:

Delhi 70 km

the position is 70 km from Delhi.

If the next stone says:

Delhi 60 km

the person has moved closer to Delhi.     

8. Motion and Rest:-An object is said to be in motion if its position changes with respect to a reference point with time.

An object is said to be at rest if its position does not change with respect to a reference point with time.     Example: Passengers in a Bus

Passengers sitting inside a moving bus are:

- At rest with respect to the bus.

- In motion with respect to buildings or trees outside the bus.

Therefore, whether an object is at rest or in motion depends on the reference point.     

9. Types of Motion:-There are three important types of motion discussed in the chapter:

A. Linear Motion

When an object moves along a straight line, its motion is called linear motion.     

Examples:

- A car moving on a straight road

- A box pushed along a straight path

- A marching student moving in a straight line

B. Circular Motion

When an object moves along a circular path, its motion is called circular motion.     

Examples:

- Merry-go-round

- A rotating wheel

- An object tied to a thread and whirled around

C. Oscillatory Motion

When an object moves to and fro about a fixed position, its motion is called oscillatory motion.     Examples:

- Swing moving to and fro

- Vibrating metal strip

- Pendulum-like motion

10. Periodic Motion

If an object repeats its path or motion after a fixed interval of time, its motion is called periodic motion.

Circular and oscillatory motions can be periodic in nature.     

11. Quick Comparison

Type of Motion                 Meaning                                                     Example

• Linear                                 Motion along a straight line                     Car on a straight road
• Circular                                 Motion along a circular path                     Merry-go-round
• Oscillatory                         To-and-fro motion about a fixed position Swing
• Periodic                                 Motion repeated after a fixed interval Swing's repeated motion

12. Important Facts to Remember

- The SI unit of length is metre (m).

- 1 km = 1000 m.

- 1 m = 100 cm.

- 1 cm = 10 mm.

- Handspan and other body-part measurements are not standard because they differ from person to person.

- A measurement consists of a number and a unit.

- A reference point is used to describe position or distance.

- Motion depends on the reference point.

- Straight-line motion is called linear motion.

- Circular-path motion is called circular motion.

- To-and-fro motion about a fixed position is called oscillatory motion.

- Motion that repeats after a fixed interval is called periodic motion.     

Let Us Enhance Our Learning – Answers

Q1. Match the lengths with the suitable units.

Column I – Length                                         Column II – Suitable Unit

(a) Distance between Delhi and Lucknow         Kilometre (km)

(b) Thickness of a coin                                         Millimetre (mm)

(c) Length of an eraser                                         Centimetre (cm)

(d) Length of school ground                                 Metre (m)

Answer:

(a) → Kilometre

(b) → Millimetre

(c) → Centimetre

(d) → Metre  

Q2. Read the statements and mark True (T) or False (F).

(i) The motion of a car moving on a straight road is an example of linear motion.

Answer: True (T)

A car moving along a straight road moves along a straight-line path, so it shows linear motion.

(ii) Any object which is changing its position with respect to a reference point with time is said to be in motion.

Answer: True (T)

An object is in motion when its position changes with respect to a reference point with time.

(iii) 1 km = 100 cm

Answer: False (F)

1 km = 1000 m = 100,000 cm.

Q3. Which of the following is not a standard unit of measuring length?

(i) millimetre

(ii) centimetre

(iii) kilometre

(iv) handspan

Answer: (iv) Handspan

Explanation: Millimetre, centimetre and kilometre are standard units of length. Handspan is a body-based unit and differs from person to person.     

Q4. Search for the different scales or measuring tapes at your home and school. Find out the smallest value that can be measured using each of these scales. Record your observations in a tabular form.

Answer:- This is an activity-based question. A sample observation table is:

Measuring instrument Smallest value that can be measured

15-cm ruler 1 mm

Metre scale 1 mm

Measuring tape 1 mm

Tailor's measuring tape 1 mm

Note: The actual smallest value may vary depending on the measuring instrument available at home or school.

Q5. Suppose the distance between your school and home is 1.5 km. Express it in metres.

We know:

1 km = 1000 m

Therefore,

1.5 km = 1.5 × 1000 m

= 1500 m

Answer: 1500 metres

Q6. Take a tumbler or a bottle. Measure the length of the curved part of the base of glass or bottle and record it.

Answer:- This is an activity-based question. The measurement will depend on the tumbler or bottle used.

Sample answer:

Length of the curved part of the base = approximately 20 cm.

A flexible measuring tape or thread can be used to measure a curved line. If a thread is used, straighten it and then measure it with a scale.     

Q7. Measure the height of your friend and express it in:

(i) metres

(ii) centimetres

(iii) millimetres

Answer:- This is an activity-based question. Suppose the height of the friend is 1.5 m.

Then:

(i) Metres = 1.5 m

(ii) Centimetres = 1.5 × 100 = 150 cm

(iii) Millimetres = 150 × 10 = 1500 mm

Answer:

(i) 1.5 m

(ii) 150 cm

(iii) 1500 mm

Q8. You are given a coin. Estimate how many coins are required to cover the length of a notebook. Verify your estimate by measuring.

Answer:- This is an activity-based question, so the answer depends on the size of the coin and notebook.

Sample answer:

Suppose:

- Length of notebook = 24 cm

- Diameter of coin = 2 cm

Number of coins required:

24 ÷ 2 = 12 coins

Therefore, approximately 12 coins are required.

The coins should be placed one after another without leaving any gap.

Q9. Give two examples each for linear, circular and oscillatory motion.

Answer:

Type of Motion Examples

• Linear motion         1. Car moving on a straight road  2. A box moving along a straight path
• Circular motion 1. Merry-go-round  2. Rotating wheel
• Oscillatory motion 1. Swing moving to and fro  2. Vibrating metal strip

The chapter defines linear motion as motion along a straight line, circular motion as motion along a circular path, and oscillatory motion as to-and-fro motion about a fixed position.     

Q10. Make a list of three objects whose lengths are conveniently expressed in mm, cm and m.

Answer:- Unit Three objects

mm Thickness of a coin, thickness of a page, thickness of a pencil lead

cm Length of an eraser, length of a pencil, length of a spoon

m Height of a person, length of a classroom, length of a school ground

Q11. A rollercoaster track is shown in Fig. 5.19. A ball starts from point A and escapes through point F. Identify the types of motion of the ball on the rollercoaster and corresponding portions of the track.

Answer:- The exact classification depends on the shape of each portion shown in Fig. 5.19. From the chapter's classification:

- Straight portion → Linear motion

- Curved circular portion → Circular motion

- To-and-fro portion → Oscillatory motion

The ball follows different types of motion according to the shape of the track at different portions.     

Q12. Tasneem wants to make a metre scale using plywood, paper, cloth, stretchable rubber and steel. Which material should she not use and why?

Answer:- She should not use paper, cloth or stretchable rubber for making a metre scale.

Reason: These materials can bend or change their length, especially stretchable rubber. A measuring scale should have a fixed and stable length so that measurements remain accurate.

Steel and suitably rigid plywood are more appropriate materials for a fixed scale.

Q13. Think, design and develop a card game on conversion of units of length to play with your friends.

Answer: Sample Activity – “Length Conversion Cards”

Make cards containing questions such as:

- 2 km = ___ m

- 5 m = ___ cm

- 300 cm = ___ m

- 7 cm = ___ mm

- 5000 m = ___ km

Rules:

1. Shuffle all the cards.

2. Each player picks one card.

3. The player solves the conversion.

4. A correct answer earns 1 point.

5. The player with the required number of correct answers wins the game.

Important conversions used in the game: