Measurement of Length and Motion — NCERT Solutions

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

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):

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.