Chapter 5 — Measurement of Length and Motion
Detailed solutions to every in-text “curiosity” question and every “Let us enhance our learning” exercise, with step-by-step unit conversions and the original textbook figures.
💭In-text Questions
Yes, all three are measuring instruments — the geometry-box scale, the metal measuring rod, and the flexible measuring tape all have markings and are used to measure length. They differ only in size and flexibility: the scale is short and rigid (usually 15 cm), the rod is long and rigid, and the tape is long and flexible so it can bend around objects.
Char angula means “four fingers’ width.” Angula is an old Indian unit of length equal to the width of one finger, so char angula = four finger-widths. Mother wanted the uniform made longer by about four fingers’ width. Being a body-based unit, it differs from person to person.
No, it would not be convenient. We should choose a unit that suits the size of what we are measuring.
- For very large lengths (e.g., railway track between cities), the metre gives huge, clumsy numbers — so we use the kilometre (1 km = 1000 m).
- For very small lengths (e.g., thickness of a page), the metre is far too big — so we use the centimetre or millimetre.
No — the results will now be the (nearly) same for everyone. A metre scale is a standard unit: its length is fixed and identical for every person.
Handspans differ from person to person, so they gave different numbers. But a metre scale does not depend on who uses it, so everyone gets the same measurement (apart from tiny errors in reading).
Because many things we need to measure are curved or not flat — such as the girth of a tree, the chest or waist for stitching clothes, or a curved edge. A stiff, rigid scale cannot bend to follow these shapes.
A flexible measuring tape can bend and wrap around curved surfaces, so it measures such lengths easily and accurately.
The kilometre stones indicate Padma’s distance (position) from Delhi, which is the reference point here.
As the bus moved, the numbers kept decreasing — 70 km → 60 km → … . A steadily decreasing distance meant Delhi was getting nearer, so Padma concluded she was getting closer to her grandparents’ house.
Yes. As time passes, Padma’s distance from Delhi keeps decreasing, so her position with respect to the reference point (Delhi) changes with time.
The position of an object changes with respect to a reference point only when the object is moving. If the object stays still, its distance from the reference point stays the same. So a change of position with time is the sign of motion.
No — you cannot tell from inside. Everything inside the ship (you, the seats, the floor) moves together with the ship, so relative to you they all stay at rest.
To detect motion you need a reference point. With no window there is no outside reference point to compare against, so a ship moving smoothly in a straight line at constant speed feels exactly the same as a stationary one. You would need to see something outside the ship to judge its motion.
📘Let us enhance our learning
| Column I (length) | Suitable unit |
|---|---|
| Distance between Delhi and Lucknow | kilometre |
| Thickness of a coin | millimetre |
| Length of an eraser | centimetre |
| Length of school ground | metre |
Big distances → km · small everyday objects → cm · very thin objects → mm · medium/large lengths → m.
- (i) The motion of a car moving on a straight road is an example of linear motion. ✓ True
- (ii) Any object changing its position with respect to a reference point with time is said to be in motion. ✓ True
- (iii) 1 km = 100 cm. ✗ False
Correct: 1 km = 1000 m and 1 m = 100 cm, so 1 km = 1,00,000 cm.
Answer: (iv) handspan. A handspan differs from person to person, so it is not a standard unit. Millimetre, centimetre and kilometre are all part of the standard SI-based system.
The smallest value a scale can measure equals its smallest division (least count) — the gap between its two closest markings. A sample record:
| Measuring device | Smallest division | Smallest value it can measure |
|---|---|---|
| 15-cm plastic scale | 1 small mark = 1 mm | 1 mm |
| Metre scale | 1 mm | 1 mm |
| Tailor’s measuring tape | usually 1 mm | 1 mm (some show only 0.5 cm) |
| Long steel measuring tape | 1 mm | 1 mm |
Your own results may vary slightly depending on the exact scales you find — record the smallest marking on each.
So the distance is 1500 metres.
A rigid scale cannot follow a curve, so use the thread method (as in Fig. 5.8):
- Wrap a thread once around the curved base of the glass/bottle and mark the point where it meets its starting end.
- Now straighten the thread and place it along a 15-cm scale (or metre scale).
- Read the length between the start and the mark — this is the length of the curved base (its perimeter).
Example: if the thread length reads 22 cm, the curved base is 22 cm long.
Suppose the measured height is 150 cm. Then:
Use your friend’s actual height in place of 150 cm and follow the same three steps.
Method: number of coins = (length of the notebook side) ÷ (diameter of one coin).
First estimate by eye, then measure the notebook side and the coin’s diameter with a 15-cm scale and divide, as above, to check how close your estimate was.
- Linear A car moving on a straight road; a stone falling straight down (also: an athlete running on a straight track).
- Circular A stone whirled on a thread; the blades of a moving ceiling fan (also: a merry-go-round; hands of a clock).
- Oscillatory A swing moving to and fro; the pendulum of a wall clock (also: a child on a see-saw; a vibrating metal strip).
| Size | Three objects |
|---|---|
| mm | Thickness of a coin · thickness of an ID/notebook page · a mustard seed / pencil-lead tip |
| cm | Length of an eraser · length of a pencil · width of a matchbox |
| m | Height of a door · length of the classroom table · height of a person |
The ball changes its type of motion along the track:
- From A to B — the ball rolls down a straight, sloping part of the track → Linear motion
- Around the loop (B/C → D → E) — the ball goes round the circular loop → Circular motion
- From E to F — the ball moves along the straight track and escapes → Linear motion
So the ball’s motion is linear, then circular (the loop), then linear again.
She should not use stretchable rubber, cloth, or paper:
- Stretchable rubber — it stretches and contracts, so the markings move and the length keeps changing → measurements become wrong.
- Cloth — it is soft and can stretch, sag or even shrink; it is not rigid, so readings are unreliable.
- Paper — it is flimsy, tears and bends easily, and can stretch when damp → not durable or accurate.
She can use plywood or steel, because they are rigid, do not stretch, and keep a fixed length — giving accurate, long-lasting measurements.
This is a fun design activity. A simple idea:
- Make matching-pair cards, e.g. one card says “1 km” and its pair says “1000 m”; “1 m” ↔ “100 cm”; “1 cm” ↔ “10 mm”; “5 km” ↔ “5000 m”, and so on.
- Shuffle and deal. On each turn a player must correctly match a value with its equal in another unit (like a memory/“snap” game).
- A correct conversion wins the pair; the player with the most pairs wins.
Use the key relations: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.