Measurement of Length and Motion

Given/Context: Some measuring devices (like measuring tapes) are made of flexible materials such as cloth or plastic.

Explanation:
Flexible measuring devices are used because not all objects have straight or flat surfaces. For example:
- The curved surface of a bottle or a ball cannot be measured with a rigid ruler.
- The length of a curved road or a body part (like the waist or chest) requires a flexible tape.

Conclusion: Some length measuring devices are made of flexible materials so that they can bend and conform to curved or irregular surfaces, allowing accurate measurement of lengths that cannot be measured with a rigid scale.

Concept: The concept of reference point is used to decide whether an object is in motion or at rest.

Answer:
An object is said to be in motion if its position changes with respect to a fixed reference point with time.

An object is said to be at rest if its position does NOT change with respect to a fixed reference point with time.

Example:
- A tree standing on the ground does not change its position with respect to the ground (reference point) → it is at rest.
- A cow walking in a field changes its position with respect to the ground → it is in motion.

Key point: The same object can be at rest with respect to one reference point and in motion with respect to another. For example, a passenger sitting in a moving bus is at rest with respect to the bus but in motion with respect to a building outside.

Given: A ship moves at constant speed in a straight line on a calm sea; there are no windows.

Concept: Motion is relative and requires a reference point. When there is no external reference point visible, and the ship moves at constant speed (no acceleration), there is no mechanical experiment that can distinguish between rest and uniform motion.

Answer: No, there is no way to determine whether the ship is moving or stationary if it moves at a constant speed in a straight line and there is no window (no external reference point visible). This is because all mechanical phenomena inside the ship will appear exactly the same whether the ship is at rest or moving at constant speed. You would need an external reference point (like a building on the shore, or looking outside) to detect the motion.

Conclusion: Without an external reference point, it is impossible to tell if the ship is moving at constant speed or is stationary.

Given: Various lengths and units to be matched.

Concept: We choose the unit that is most appropriate for the magnitude of the length being measured.

Matching:

| Column I | Column II |
|---|---|
| Distance between Delhi and Lucknow | kilometre |
| Thickness of a coin | millimetre |
| Length of an eraser | centimetre |
| Length of school ground | metre |

Justification:
- Delhi to Lucknow is hundreds of kilometres, so km is appropriate.
- A coin is very thin (about 1–2 mm), so mm is appropriate.
- An eraser is a few centimetres long, so cm is appropriate.
- A school ground is tens of metres long, so m is appropriate.

Concept: Definitions of linear motion, motion, and unit conversions.

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

Answer: True (T)

Justification: Linear motion is defined as motion along a straight line. A car moving on a straight road moves along a straight-line path, so it is linear motion.

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(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)

Justification: This is the exact definition of motion — if an object's position changes with respect to a reference point over time, it is in motion.

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(iii) $1\mathrm{km} = 100\mathrm{cm}$

Answer: False (F)

Justification: The correct conversion is:
$$1\mathrm{km} = 1000\mathrm{m} = 1000 \times 100\mathrm{cm} = 1{,}00{,}000\mathrm{cm}$$
So $1\mathrm{km} = 1{,}00{,}000\mathrm{cm}$, not $100\mathrm{cm}$.

Correct Answer: (iv) handspan

Justification: Millimetre (mm), centimetre (cm), and kilometre (km) are all standard SI units of length that are universally accepted and give the same measurement regardless of who measures. A handspan, however, varies from person to person (it depends on the size of the individual's hand), so it is not a standard unit of measurement. It is an example of a non-standard or arbitrary unit.

Given: This is an activity-based observation question. A sample answer is provided below.

Concept: The smallest value that can be measured by a scale is determined by the smallest division marked on it.

Sample Observation Table:

| S. No. | Scale/Measuring Tape | Smallest Division (Least Count) |
|---|---|---|
| 1 | 15-cm plastic scale (school) | 1 mm |
| 2 | 30-cm wooden ruler | 1 mm |
| 3 | Cloth measuring tape (tailor's) | 1 mm |
| 4 | Steel measuring tape (carpenter's) | 1 mm |
| 5 | Metre scale (laboratory) | 1 mm |

Conclusion: Most common scales have a least count (smallest measurable value) of 1 mm (0.1 cm). This means lengths smaller than 1 mm cannot be accurately measured using these scales.

Given: Distance = $1.5\,\mathrm{km}$

Formula/Conversion:
$$1\,\mathrm{km} = 1000\,\mathrm{m}$$

Calculation:
$$1.5\,\mathrm{km} = 1.5 \times 1000\,\mathrm{m}$$
$$= 1500\,\mathrm{m}$$

Answer: The distance between school and home is $\mathbf{1500\,m}$.

Given: This is a hands-on activity question.

Concept: A curved length (like the circumference of the base of a glass) cannot be measured directly with a rigid ruler. A flexible measuring tape or a thread is used.

Method:
1. Take a thread and carefully place it along the curved edge (circumference) of the base of the tumbler/bottle, going all the way around.
2. Mark the point on the thread where it completes one full circle.
3. Straighten the thread and measure its length using a ruler.

Sample Result:
- For a standard tumbler with base diameter ≈ 7 cm:
$$\text{Circumference} = \pi \times d = 3.14 \times 7 \approx 22\,\mathrm{cm}$$

Record: The length of the curved part (circumference) of the base of the tumbler = approximately 22 cm (this value will vary depending on the tumbler used).

Note: Students should record the actual measured value from their own tumbler/bottle.

Given: This is an activity-based question. A sample calculation is shown.

Assume the measured height of the friend = $1.45\,\mathrm{m}$ (sample value; students should use their actual measurement).

Conversions:

(i) In metres:
$$\text{Height} = 1.45\,\mathrm{m}$$

(ii) In centimetres:
$$1\,\mathrm{m} = 100\,\mathrm{cm}$$
$$1.45\,\mathrm{m} = 1.45 \times 100 = 145\,\mathrm{cm}$$

(iii) In millimetres:
$$1\,\mathrm{cm} = 10\,\mathrm{mm}$$
$$145\,\mathrm{cm} = 145 \times 10 = 1450\,\mathrm{mm}$$

Answer:
- Height = $1.45\,\mathrm{m}$ = $145\,\mathrm{cm}$ = $1450\,\mathrm{mm}$

*(Students should substitute their own measured value and perform the same conversions.)*

Given: A coin and a notebook.

Step 1 – Estimation:
Look at the coin and the notebook side. Visually estimate how many coins would fit along the length of the notebook side.

*(Sample estimate: approximately 15–20 coins)*

Step 2 – Measurement:
- Measure the diameter of the coin using the 15-cm scale.
- Sample: Diameter of a 1-rupee coin ≈ $2.5\,\mathrm{cm}$
- Measure the length of the chosen side of the notebook.
- Sample: Length of notebook side ≈ $28\,\mathrm{cm}$

Step 3 – Calculation:
$$\text{Number of coins} = \frac{\text{Length of notebook side}}{\text{Diameter of coin}}$$
$$= \frac{28\,\mathrm{cm}}{2.5\,\mathrm{cm}} = 11.2 \approx 11\,\text{coins}$$

Step 4 – Verification:
Place the coins one after another along the notebook side and count. The count should match the calculated value.

Conclusion: The number of coins required = approximately 11 coins (this will vary based on the actual coin and notebook used). The estimated and calculated values should be close to each other.

Concept: Types of motion are classified based on the path followed by the object.

Linear Motion (motion along a straight line):
1. A ball rolling along a straight road.
2. A train moving on a straight railway track.

Circular Motion (motion along a circular path):
1. A child sitting on a merry-go-round.
2. The blades of a rotating fan.

Oscillatory Motion (to and fro motion about a fixed position):
1. The motion of a swing (jhula).
2. The pendulum of a wall clock moving to and fro.

Concept: We choose the unit that best suits the size of the object — mm for very small objects, cm for medium-sized objects, and m for large objects.

Table 5.6: Sizes of objects around us

| Size | Objects |
|---|---|
| mm | Thickness of a coin, thickness of a SIM card, width of a pencil lead |
| cm | Length of an eraser, length of a pen, width of a notebook |
| m | Height of a door, length of a classroom, height of a person |

Justification:
- Objects measured in mm: very small objects where even 1 cm would be too large a unit.
- Objects measured in cm: everyday small objects that are a few to tens of centimetres.
- Objects measured in m: large objects like furniture, rooms, or a person's height.

Given: A ball travels along a rollercoaster track from point A to point F. (Note: The figure shows a track with straight sections, a circular loop, and curved portions.)

Concept: The type of motion depends on the shape of the path:
- Straight path → Linear motion
- Circular path → Circular motion
- To and fro path → Oscillatory motion

Identification of motion along the track (based on a typical rollercoaster shape with straight sections and a circular loop):

| Portion of Track | Type of Motion |
|---|---|
| Straight sections (e.g., A to B, E to F) | Linear motion |
| Circular loop (e.g., C to D — the loop portion) | Circular motion |
| Curved/sloping sections (transitions) | Curvilinear motion (combination) |

Answer:
- On the straight portions of the track: the ball undergoes linear motion.
- On the circular loop portion of the track: the ball undergoes circular motion.

*(Since the exact figure is not visible, students should apply the above logic to the specific portions labeled A through F in their textbook figure.)*

Given: Materials considered — plywood, paper, cloth, stretchable rubber, steel.

Concept: A good measuring scale must be rigid (not flexible or stretchable) and must not change its length under normal conditions of use.

Materials she should NOT use:

1. Stretchable rubber — It stretches when pulled, so the markings on it will not remain at fixed distances. This will give incorrect measurements.

2. Cloth — Cloth can stretch, shrink (especially when wet), or sag, making measurements unreliable.

3. Paper — Paper can tear easily, absorb water and expand, or crumple, making it unsuitable for a durable and accurate scale.

Materials she CAN use:
- Plywood — rigid and does not stretch.
- Steel — rigid, durable, and does not stretch.

Conclusion: Tasneem should not use stretchable rubber, cloth, and paper because these materials can change their shape or length, leading to inaccurate measurements. A good scale must be made of a rigid, non-stretchable material like plywood or steel.

Given: This is a creative/project-based question.

Sample Card Game Design: 'Length Ludo'

Objective: Convert units of length correctly and be the first to collect all four unit cards (mm, cm, m, km).

Materials needed: Index cards (at least 40), pen/marker.

How to make the cards:
- Question Cards (30 cards): Write a length in one unit on each card.
- Examples:
- "$5\,\mathrm{km} = ?\,\mathrm{m}$" (Answer: 5000 m)
- "$250\,\mathrm{cm} = ?\,\mathrm{m}$" (Answer: 2.5 m)
- "$3\,\mathrm{m} = ?\,\mathrm{cm}$" (Answer: 300 cm)
- "$15\,\mathrm{mm} = ?\,\mathrm{cm}$" (Answer: 1.5 cm)
- Answer Cards (30 cards): Write the corresponding answer.
- Unit Cards (4 cards): mm, cm, m, km — one each.

How to play:
1. Shuffle question cards and place face down.
2. Each player picks a card and answers the conversion.
3. If correct (verified by answer card), the player keeps the card.
4. The player with the most correct answers wins a Unit Card.
5. The first player to collect all 4 Unit Cards wins.

Key conversions to include on cards:
$$1\,\mathrm{km} = 1000\,\mathrm{m}$$
$$1\,\mathrm{m} = 100\,\mathrm{cm}$$
$$1\,\mathrm{cm} = 10\,\mathrm{mm}$$
$$1\,\mathrm{m} = 1000\,\mathrm{mm}$$

Learning outcome: Students practise unit conversions in a fun, interactive way.