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Measurement of Length and Motion

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Chapter Notes

Overview
This chapter introduces the concept of measurement, focusing on length, and explains why standard units are necessary. It covers the correct way to measure length using a scale, how to measure curved lines, and how to describe the position of an object using a reference point. The chapter then explores the concept of motion, defining it as a change in position with respect to a reference point over time, and classifies motion into linear, circular, and oscillatory types. The one big idea a student must walk away with is that accurate measurement requires a standard unit (the metre) and a correct method, and that motion is always described relative to a chosen reference point.
Key Concepts (16)
Measurement
The process of determining the length, size, or amount of something using a standard unit.
e.g. Measuring the length of a table using a metre scale to find it is 1.5 metres long.
Unit
A standard quantity used to express a measurement, consisting of a number and a unit name.
e.g. In '13 handspans', 13 is the number and 'handspan' is the unit.
Handspan
The distance between the tip of the thumb and the tip of the little finger when the hand is fully stretched; an example of a non-standard unit of length.
e.g. Deepa's mother used her handspan (called 'balisht') to measure cloth.
Angula
An ancient Indian unit of length equal to the width of a finger, still used by some traditional craftspeople like carpenters and tailors.
e.g. Deepa's mother asked the tailor to increase the uniform length by 'char angula' (four fingers width).
International System of Units (SI units)
The modern, globally accepted system of standard units of measurement adopted by countries to avoid confusion.
e.g. The SI unit of length is the metre (m).
Metre (m)
The SI unit of length; one metre is divided into 100 equal parts called centimetres.
e.g. A metre scale is used to measure the height of a room.
Centimetre (cm)
A unit of length equal to one-hundredth of a metre (1 m = 100 cm).
e.g. A 15-cm scale is commonly used in geometry boxes.
Millimetre (mm)
A unit of length equal to one-tenth of a centimetre (1 cm = 10 mm); the smallest value measurable using a standard 15-cm scale.
e.g. The thickness of a coin is measured in millimetres.
Kilometre (km)
A unit of length equal to 1000 metres, used for measuring large distances.
e.g. The distance between Delhi and Lucknow is measured in kilometres.
Reference point
A fixed object or point with respect to which the position or distance of another object is stated.
e.g. Delhi is the reference point when a kilometre stone reads 'Delhi 70 km'.
Motion
An object is said to be in motion if its position changes with respect to a reference point over time.
e.g. A bus moving on a road is in motion relative to a building on the side of the road.
Rest
An object is said to be at rest if its position does not change with respect to a reference point over time.
e.g. Passengers seated inside a moving bus are at rest relative to the bus itself.
Linear motion
Motion along a straight line.
e.g. A car moving on a straight road, or a heavy box being pushed in a straight line.
Circular motion
Motion along a circular path.
e.g. A merry-go-round, or an eraser tied to a thread and whirled around.
Oscillatory motion
Motion that moves to and fro about a fixed position.
e.g. A swing moving back and forth, or a hanging eraser released from one side.
Periodic motion
Motion that repeats its path after a fixed interval of time.
e.g. Both circular motion (e.g., a merry-go-round) and oscillatory motion (e.g., a swing) are periodic.
How It Works
Measuring length using a standard scale
  1. Place the scale in contact with the object along its entire length (Fig. 5.4a).
  2. Ensure the eye is positioned directly above the point being read (position B in Fig. 5.5) to avoid parallax error.
  3. Read the marking at the end of the object. If the zero mark is broken, use any full mark (e.g., 1.0 cm) and subtract that reading from the reading at the other end.
  4. Record the measurement as a number followed by the unit (e.g., 9.4 cm).
💡 Always place the scale flat against the object and keep your eye directly above the reading point. If the scale end is broken, do not start from the broken edge; subtract the starting mark from the ending mark.
Measuring the length of a curved line
  1. Take a flexible thread and place it along the curved line, following its shape exactly.
  2. Mark the point on the thread that matches the end of the curved line.
  3. Straighten the thread carefully.
  4. Measure the length of the straightened thread using a metre scale.
💡 The thread must follow every curve without stretching. A flexible measuring tape can also be used directly.
Describing position using a reference point
  1. Choose a fixed object or point as the reference point (e.g., a bus stand, Delhi).
  2. Measure the distance of the object from this reference point.
  3. State the position as the distance from the reference point (e.g., '70 km from Delhi').
💡 The reference point must be fixed. Different reference points give different descriptions of position, as seen when Deepa and her friends compared distances from their houses versus from the bus stand.
Determining if an object is in motion or at rest
  1. Choose a reference point.
  2. Observe the object over a period of time.
  3. If the object's position changes with respect to the reference point, it is in motion.
  4. If the object's position does not change with respect to the reference point, it is at rest.
💡 Motion is relative. The same object can be in motion relative to one reference point and at rest relative to another. For example, passengers in a bus are at rest relative to the bus but in motion relative to a building outside.
Exam Traps — Don't Make These Mistakes
⚠ Writing the unit incorrectly
✗ 10 K.M. or 10 Kms or 10 km.
→ Symbols for units are written in lowercase (except at the start of a sentence), never followed by 's' for plural, and a full stop is not written after the symbol unless it is the end of a sentence.
✓ 10 km (with a space between the number and the symbol, no capital letters, no 's', no full stop).
⚠ Confusing motion and rest without specifying a reference point
✗ The passengers in the bus are in motion.
→ The statement is incomplete because motion is relative. Without specifying the reference point, the answer is ambiguous.
✓ The passengers in the bus are at rest with respect to the bus, but in motion with respect to a building outside the bus.
⚠ Using a broken scale incorrectly
✗ The length of the object is 10.4 cm (reading from a broken scale where the zero mark is missing).
→ If the zero mark is broken, you cannot start measuring from the broken edge. You must start from a full mark (e.g., 1.0 cm) and subtract that value from the final reading.
✓ The length of the object is 10.4 cm – 1.0 cm = 9.4 cm.
⚠ Mixing up conversion factors
✗ 1 km = 100 m or 1 m = 1000 cm
→ The correct conversions are: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm. Students often confuse the number of zeros.
✓ 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
⚠ Calling all non-straight motion 'circular'
✗ The motion of a swing is circular motion.
→ A swing moves to and fro along a curved path, but it does not complete a full circle. This is oscillatory motion, not circular motion.
✓ The motion of a swing is oscillatory motion because it moves to and fro about a fixed position.
Compare & Contrast
Consistency of measurement
Standard unit (e.g., metre)
Non-standard unit (e.g., handspan)
A standard unit (metre) gives the same measurement for the same length regardless of who measures it, while a non-standard unit (handspan) varies from person to person because body parts differ in size.
Path of motion
Circular motion
Oscillatory motion
In circular motion, an object moves along a complete circular path (e.g., a merry-go-round), while in oscillatory motion, an object moves to and fro about a fixed position without completing a full circle (e.g., a swing).
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 Very Short Answer (1 mark), 1 Short Answer (3 marks), 1 Long Answer (5 marks) — total approximately 10-12 marks.
Most asked: Conversion of units (km to m, m to cm, cm to mm) · Correct method of measuring length (placement of scale, eye position, broken scale) · Definition and examples of linear, circular, and oscillatory motion · Concept of reference point and relative motion
Don't skip: Numerical problems on unit conversion (e.g., 'Express 1.5 km in metres'); Describing the correct method to measure length using a scale with a broken end; Classifying different motions (linear, circular, oscillatory) with examples from everyday life; Explaining why motion is relative using a reference point
One-Line Revision (read aloud before the exam)
  1. The SI unit of length is the metre (m).
  2. 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
  3. A handspan is a non-standard unit that varies from person to person.
  4. Always place the scale in contact with the object along its entire length.
  5. Keep your eye directly above the reading point to avoid parallax error.
  6. If the zero mark of a scale is broken, subtract the starting mark from the final reading.
  7. To measure a curved line, use a flexible thread and then measure the straightened thread.
  8. A reference point is a fixed object or point used to describe the position of another object.
  9. An object is in motion if its position changes with respect to a reference point over time.
  10. An object is at rest if its position does not change with respect to a reference point over time.
  11. Motion is relative; the same object can be in motion relative to one reference point and at rest relative to another.
  12. Linear motion is motion along a straight line, e.g., a car on a straight road.
  13. Circular motion is motion along a circular path, e.g., a merry-go-round.
  14. Oscillatory motion is to-and-fro motion about a fixed position, e.g., a swing.
  15. Both circular and oscillatory motions are periodic because they repeat after a fixed interval of time.

MCQs — 10 Questions with Answers

Q1. Deepa's mother asked the tailor to increase the uniform length by char angula. What does char angula mean?

  • A. Four finger widths ✓
  • B. Four metres of cloth
  • C. Four handspans
  • D. Four centimetres

Answer: A — Char means four and angula means finger width in traditional Indian measurement.

Q2. When Deepa and her friends measured the classroom table using handspans, why did they get different numbers?

  • A. The table was not straight
  • B. Each student's handspan was a different size ✓
  • C. They measured at different times
  • D. They used different scales

Answer: B — Handspan differs from person to person, so each student got a different measurement for the same table.

Q3. What is the SI unit of length?

  • A. Centimetre
  • B. Millimetre
  • C. Metre ✓
  • D. Angula

Answer: C — Metre (m) is the international standard unit of length accepted worldwide.

Q4. How many centimetres are equal to 1 metre?

  • A. 10 cm
  • B. 100 cm ✓
  • C. 1000 cm
  • D. 50 cm

Answer: B — By definition, 1 metre is divided into 100 equal parts called centimetres.

Q5. Fill in the blank: 1 cm = _____ mm

  • A. 100 mm
  • B. 10 mm ✓
  • C. 1 mm
  • D. 0.1 mm

Answer: B — Each 1 cm section on a scale is further divided into 10 equal parts of 1 mm each.

Q6. If you want to measure the length of your pencil, which scale would be most suitable?

  • A. A 1 metre long scale
  • B. A 15 cm scale ✓
  • C. A 1 kilometre measuring tape
  • D. A flexible tailor's tape

Answer: B — A 15 cm scale is ideal for small objects like pencils; a full metre scale would be too large and inconvenient.

Q7. When measuring the length of a pencil with a scale, where should you position your eye?

  • A. To the side of the pencil
  • B. Below the pencil at an angle
  • C. Directly above the tip of the pencil ✓
  • D. Far away from the scale

Answer: C — Positioning your eye directly above ensures you read the correct measurement without parallax error.

Q8. Your scale's zero marking is broken. To measure a pencil, you align one end at 2 cm and the other at 18 cm. What is the length of the pencil?

  • A. 18 cm
  • B. 20 cm
  • C. 16 cm ✓
  • D. 2 cm

Answer: C — When the zero is broken, subtract the smaller reading from the larger: 18 cm − 2 cm = 16 cm.

Q9. Why did different countries decide to use a single International System of Units (SI)?

  • A. To make measurements more difficult
  • B. To reduce the number of units available
  • C. To avoid confusion when people travelled and traded between countries ✓
  • D. Because ancient India used only one unit

Answer: C — When people started travelling and trading, having different units in each place created confusion, so one standard system was adopted.

Q10. Which of the following statements is true?

  • A. A handspan is a standard unit that everyone has the same size
  • B. A metre is a standard unit that means the same length everywhere ✓
  • C. A centimetre is larger than a millimetre by 100 times
  • D. A flexible tape is better than a scale for measuring straight pencils

Answer: B — A metre is defined as exactly 100 cm everywhere in the world, unlike body parts which vary in size.

Flashcards

What is a unit of measurement?

A unit is a standard amount used to measure and compare the length or size of objects, like metre, centimetre, or handspan.

Why do different students get different handspan measurements for the same table?

Because each student's handspan is a different size, so using body parts as units gives different numbers.

What is the SI unit of length?

The metre (m) is the SI unit of length, which is the international standard measurement used worldwide.

How many centimetres are in 1 metre?

1 metre = 100 centimetres.

What does 1 mm equal in centimetres?

1 millimetre = 0.1 centimetre (or 1 mm = one-tenth of 1 cm).

What is the correct eye position when measuring length with a scale?

Your eye should be directly above the tip or end of the object you are measuring.

How do you measure length if the zero end of your scale is broken?

Use any clear marking on the scale (like 1.0 cm), measure to the other end, then subtract: final length = larger reading − smaller reading.

Why did ancient Indians use angula (finger width) for measurement?

Angula was a traditional unit used by craftspeople like carpenters and tailors before modern standard units were created.

Which measuring tool is better: a ruler or a tailor's tape?

A ruler is better for straight objects like pencils; a tailor's flexible tape is better for curved things like chest or tree girth.

Why was the International System of Units (SI) created?

When people started travelling between countries, different measurement units caused confusion, so countries agreed on one standard SI system.

Important Board Questions

What is a unit of measurement? Give one example. [1 mark]

A unit is a standard amount we use to measure things. Examples: metre, centimetre, handspan, foot.

Why did Deepa's friends get different handspan measurements for the same classroom table? Explain in 2-3 sentences. [2 marks]

Think about why handspans differ from person to person, and how this affects measurement results when using body parts as units.

Explain with a daily Indian example why standard units like metre and centimetre are better than body parts like handspan or foot for measuring length. (Hint: Think of a tailor or shopkeeper.) [3 marks]

Compare measurements by different people using body parts vs. using metre scale. A shopkeeper selling 2 metres of cloth gets the same length no matter who measures it with a metre scale, but different lengths if people use their own handspans.

Your metre scale has a broken zero end. Explain the steps you would follow to measure the length of your notebook using this broken scale. Include an example calculation. [5 marks]

Find any clear marking on the scale (like 1 cm or 2 cm), align notebook ends to two clear marks, read both markings, then subtract smaller from larger marking. Example: if notebook aligns from 3 cm to 28 cm, length = 28 − 3 = 25 cm.

True or False: 'A flexible measuring tape and a metre scale are suitable for measuring the same types of objects.' Give one reason for your answer. [2 marks]

A scale is for straight objects (pencil, book), tape is for curved objects (chest, tree girth). They measure different types of things, so the statement is false.

Assertion-Reason Questions for Measurement of Length and Motion

Q1. Assertion (A):

The SI unit of length is metre, and it is used internationally for all measurements.

Reason (R):

The SI unit was adopted by different countries to avoid confusion when people travelled between places with different measurement systems.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both assertion and reason are true, and the reason correctly explains why the SI unit was adopted. Countries came together to create one standard system because different systems caused confusion in trade and travel.

Q2. Assertion (A):

When using a scale to measure length, your eye should be directly above the object being measured.

Reason (R):

This position helps you see the markings on the scale more clearly from a distance.

Answer: C — A is true but R is false — The assertion is true, but the reason is incorrect. The correct reason is that positioning your eye directly above prevents parallax error, which would give an inaccurate reading. It's not just about seeing the markings more clearly.

Q3. Assertion (A):

A metre scale cannot be used to measure the length of a curved line accurately.

Reason (R):

A metre scale is rigid and straight, so it cannot follow the curves of a curved line.

Answer: A — Both A and R are true, and R is the correct explanation of A — Since the rigid metre scale cannot bend along the curve, it cannot measure the curved length accurately, and the reason correctly explains why.

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Case-Based Questions (CBQ) for Measurement of Length and Motion

Case Study:

Rajesh is preparing to buy a new school uniform from a tailor shop in Mumbai. His mother takes him to the tailor. The tailor measures Rajesh's height using a flexible measuring tape and notes that he is 145 centimetres tall. Then the tailor measures the length of cloth needed by using the same tape, measuring from Rajesh's shoulder to his knee. The tailor writes down the measurement as 65 cm for the shirt length. Later, Rajesh's younger sister Priya also wants a uniform made by the same tailor. When the tailor measures Priya using the same flexible tape, he finds she needs 55 cm of cloth for her shirt.

Q1. Why did the tailor use a flexible measuring tape instead of a rigid metre scale?

  • A. Because it was cheaper
  • B. Because it could bend around the body and give accurate measurements without gaps ✓
  • C. Because it was faster to use
  • D. Because metre scales are not allowed in tailor shops

Answer: B

Q2. What is the main reason Priya's shirt length (55 cm) is different from Rajesh's shirt length (65 cm)?

  • A. The tailor made a mistake in measurement
  • B. Priya is younger and shorter than Rajesh, so needs less cloth ✓
  • C. Flexible tape measures differently for girls
  • D. The shop had limited cloth for Priya

Answer: B

Q3. If the tailor had used handspan to measure the cloth instead of a tape measure, what problem might he have faced?

  • A. Handspan would be more accurate
  • B. Different handspans are different sizes, so measurements would be unreliable and inconsistent ✓
  • C. Handspan would measure faster
  • D. Handspan is the official unit for tailoring

Answer: B

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