Measurement of Length and Motion

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measuring rod

measuring tape

balisht

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centimetre

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1000

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reference point

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linear

oscillatory

periodic

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A–3, B–1, C–2, D–5, E–4

A–2, B–1, C–5, D–3, E–4

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Hint: Body parts differ from person to person, so the same length gives different numbers of handspans for different people.

Hint: Metre (m); 1 m = 100 cm and 1 cm = 10 mm.

Hint: Body-based units vary, causing confusion when people travel; standard units give the same result everywhere.

Hint: Place the scale in contact with the object along its length, with the zero mark aligned to one end.

Hint: Directly above the point being read; otherwise the reading is incorrect due to parallax.

Hint: Align the pencil with any full mark (say 1.0 cm), read the other end, and subtract the starting mark.

Hint: Use a thread or flexible measuring tape along the curve, then straighten and measure with a metre scale.

Hint: A fixed object/point with respect to which distance is stated; e.g., Delhi on a kilometre stone.

Hint: When its position changes with respect to a reference point with time.

Hint: Linear — car on a straight road, dropped eraser; Circular — merry-go-round, whirled eraser on a thread.

Hint: To-and-fro motion about a fixed position; e.g., a swing or a hanging eraser released to one side.

Hint: Motion that repeats its path after a fixed interval of time; e.g., circular motion of a merry-go-round.

Hint: 1.5 km = 1500 m; 50 mm = 5 cm.

Hint: The chest is curved; a flexible tape bends around it whereas a rigid metre scale cannot.

Hint: Angula, dhanusa (also yojana).

Hint: Symbols (km, m, cm, mm) are lowercase, never followed by 's' for plural, and no full stop except at the end of a sentence.

Hint: A device attached to a bicycle wheel, used for measuring distances (e.g., in road-running races).

Hint: The stones showed decreasing distances (Delhi 70 km, then 60 km), so her position was changing with respect to the reference point Delhi.

Hint: With no external reference point, the position relative to the ship does not change, so motion cannot be detected.

Hint: Anish, Hardeep, Padma, Tasneem (and Deepa herself).

Introduction: Body parts differ in size from person to person, making them unreliable as units of length.
Key Points:
1. Different sizes — Handspan, foot and finger lengths differ from person to person.
2. Different results — The same table gave 13 and 14 handspans for Padma and Anish respectively.
3. Confusion results — The same length measured by different people gives different numbers, causing confusion.
Conclusion: We need standard units so that the same length gives the same measurement for everyone.

Introduction: Correct scale use involves proper placement and correct eye position while reading.
Key Points:
1. Place the scale correctly — Place the scale in contact with the object along its length.
2. Align the zero mark — Align the zero mark of the scale with one end of the object.
3. Eye position — Keep the eye directly above the other end while noting the reading with units.
Conclusion: Correct placement and a vertical eye position give accurate, reliable length measurements.

Introduction: When a scale's zero mark is broken, any full mark can be used with subtraction.
Key Points:
1. Starting mark — The pencil's first end lies at the 2.0 cm mark of the broken scale.
2. End mark — The pencil's other end lies at the 13.6 cm mark of the same scale.
3. Calculation — Length = 13.6 cm − 2.0 cm = 11.6 cm.
Conclusion: Subtract the starting full mark from the end reading to get the correct length, 11.6 cm.

Introduction: Motion is grouped into linear, circular and oscillatory types based on the path taken.
Key Points:
1. Linear motion — An object moves along a straight line, like a car on a straight road.
2. Circular motion — An object moves along a circular path, like a merry-go-round.
3. Oscillatory motion — An object moves to and fro about a fixed position, like a swing.
Conclusion: Identifying the path of motion tells us which of the three types it belongs to.

Introduction: Whether objects are at rest or in motion depends upon the chosen reference point.
Key Points:
1. Reference point — A fixed object or point with respect to which position or distance is stated.
2. Inside the bus — With the bus as reference, seated passengers' positions do not change; they are at rest.
3. Outside the bus — With an outside building as reference, the passengers and bus are in motion.
Conclusion: Rest and motion are decided by comparing position changes with the reference point.

Introduction: Different regions used different unit systems, which created many problems for people.
Key Points:
1. Many systems existed — Several systems of units evolved in different parts of the world.
2. Travellers' confusion — When people travelled, different regional units created a lot of confusion.
3. Common standard — Countries came together and adopted standard units, called SI units, for uniformity.
Conclusion: The SI system ensures measurements mean the same thing everywhere in the world.

Introduction: A curved line cannot be measured directly with a straight scale, so a thread helps.
Key Points:
1. Place the thread — Place a thread carefully along the entire curved line's path.
2. Mark and straighten — Mark the thread at the curve's two ends, then straighten the thread.
3. Measure the thread — Measure the straightened thread's length using a metre scale.
Conclusion: The thread's length equals the curved line's length, like measuring arch string lights.

Introduction: Length units are related by three simple conversions and are used for different sizes.
Key Points:
1. The conversions — 1 km = 1000 m, 1 m = 100 cm and 1 cm = 10 mm.
2. Small lengths — Millimetres suit tiny thicknesses like a book page; centimetres suit pencils and erasers.
3. Large lengths — Metres suit room heights; kilometres suit large distances like between cities.
Conclusion: Choosing the right unit makes every length easy to express and understand.

Introduction: Motions that repeat their paths after fixed time intervals are called periodic.
Key Points:
1. Periodic motion — If an object repeats its path after a fixed interval of time, it is periodic.
2. Circular repetition — A whirled eraser or merry-go-round repeats its circular path again and again.
3. Oscillatory repetition — A swing or hanging eraser repeats its to-and-fro motion regularly.
Conclusion: Both circular and oscillatory motions repeat after fixed intervals, so both are periodic.

Introduction: Unit conversions help express a mixed distance in a single unit.
Key Points:
1. Convert kilometres — 2 km = 2 × 1000 m = 2000 m.
2. Add metres — Total distance = 2000 m + 250 m = 2250 m.
3. Convert to centimetres — 2250 m = 2250 × 100 cm = 2,25,000 cm.
Conclusion: Therefore, 2 km 250 m equals 2250 m, which equals 2,25,000 cm.

Introduction: Special scales enable visually challenged students to measure lengths independently.
Key Points:
1. Raised markings — They use scales with raised markings that can be felt by touching them.
2. Feeling the marks — Running fingers along the raised marks tells the measurement reading.
3. Independence — Such scales let them measure lengths without needing anyone's help.
Conclusion: Touch-based scales make length measurement possible for visually challenged students.

Introduction: A bicycle can measure road distances using a simple sound-making arrangement.
Key Points:
1. Attach the strip — Fix a flexible metal strip on a wheel spoke so it hits the frame each turn.
2. Count the sounds — Ride slowly and count the sounds; each sound means one wheel turn.
3. Calculate distance — Multiply the wheel's outer boundary length by the number of turns.
Conclusion: This method measures distances, like the Jones Counter used for road-running races.

Introduction: The same table gives different handspan numbers because handspans differ in size.
Key Points:
1. Same length — The table's length is exactly the same for both Anish and Padma.
2. Different units — Their handspans are of different sizes, working as different units.
3. Different numbers — Smaller handspans fit more times, so the numbers differ between people.
Conclusion: The number differs because the unit (handspan) differs, not the table's actual length.

Introduction: A metre scale must be made of a material with suitable measurement properties.
Key Points:
1. Rigid material — The scale must not stretch, so plywood or steel is suitable, not rubber.
2. Clear markings — Markings must be clear, permanent and easy to read for accurate measurements.
3. Durability — The material should be long-lasting, like steel or plywood, for years of use.
Conclusion: Paper, cloth and stretchable rubber must not be used as they bend, tear or stretch.

Introduction: Units and symbols of length must be written following certain standard rules.
Key Points:
1. Lowercase writing — Unit names begin with lowercase letters, except at a sentence's beginning.
2. No plural 's' — Symbols km, m, cm and mm are lowercase and never take 's' for plural.
3. Space and full stops — Leave a space between number and unit; no full stop after symbols except sentence ends.
Conclusion: Writing '7 m' correctly shows proper scientific measurement notation.

Hint: (a) Handspans are of different sizes; (b) Body-based units vary from person to person and are unreliable; (c) Use standard SI units like the metre so measurements are the same for everyone.

Hint: (a) Delhi; (b) The distance on the stones is decreasing; (c) Motion is change of position with respect to a reference point with time — Padma is in motion with respect to Delhi.

Hint: (a) The end/zero mark is broken or unclear; (b) Length = final reading − initial reading; (c) 10.4 cm − 1.0 cm = 9.4 cm.

Hint: (a) No, a rigid rod cannot follow a curve; (b) Flexible measuring tape and thread; (c) Lay thread along the curve, mark the ends, straighten it and measure with a metre scale.

Hint: (a) Slide — linear; merry-go-round — circular; swing — oscillatory; (b) Circular and oscillatory are periodic because they repeat their paths after fixed intervals.

Hint: (a) Stretchable rubber — it changes length and gives inconsistent measurements; (b) Steel and plywood — rigid, durable and hold clear markings.

Hint: (a) Their positions were not changing with respect to the bus; (b) Their positions were changing with respect to outside objects; (c) Rest and motion are relative and depend on the reference point chosen.

Hint: (a) Millimetre (mm); (b) 1 mm = 0.1 cm; (c) 1 mm.

Hint: (a) Straight track sections — linear; (b) Loop sections — circular; (c) Pendulum/swinging section — oscillatory, as it moves to and fro about a fixed position.

Hint: (a) A reference point on the ground from which to measure; (b) So all distances are measured from the same fixed point and lines are accurate; (c) A longer measuring tape, because the court is large and a 15-cm scale is too short.

Introduction: Standard units are needed because body-based units give different results for different people.
Key Points:
1. Body units vary — Handspan, foot and finger lengths differ from person to person, confusing measurements.
2. Travellers' confusion — Different regional unit systems also confused people moving between places.
3. SI adoption — Countries together adopted the International System of Units for uniform measurements worldwide.
4. SI unit of length — The SI unit of length is the metre; its symbol is m.
5. Unit relations — 1 km = 1000 m, 1 m = 100 cm and 1 cm = 10 mm link all length units.
Conclusion: Standard SI units make measurements uniform, reliable and comparable across the world.

Introduction: Accurate length measurement needs correct scale placement, eye position and reading method.
Key Points:
1. Scale placement — Place the scale in contact with the object along its entire length.
2. Eye position — Keep the eye directly above the tip of the object's other end while reading.
3. Broken zero mark — Use any full mark, like 1.0 cm, and subtract it from the end reading.
4. Worked example — Readings of 1.0 cm and 10.4 cm give length = 10.4 cm − 1.0 cm = 9.4 cm.
5. Write with units — Always write the unit with the number, like 9.4 cm, for a complete measurement.
Conclusion: Following these steps gives correct length measurements even with a broken scale.

Introduction: Motion is classified as linear, circular or oscillatory based on the object's path.
Key Points:
1. Linear motion — Motion along a straight line, like an eraser dropping or a car on a straight road.
2. Circular motion — Motion along a circular path, like a whirled eraser or a merry-go-round.
3. Oscillatory motion — To-and-fro motion about a fixed position, like a swing or hanging eraser.
4. Periodic circular — Circular motion repeats its circular path after fixed intervals of time.
5. Oscillatory is periodic too — Oscillatory motion also repeats its to-and-fro path regularly.
Conclusion: Circular and oscillatory motions are periodic, while linear motion generally is not.

Introduction: A reference point is a fixed point with respect to which distances and positions are described.
Key Points:
1. Definition — When distance is stated with respect to a fixed object or point, it is a reference point.
2. Padma's journey — Kilometre stones reading 'Delhi 70 km' then 'Delhi 60 km' showed her nearing Delhi.
3. Delhi as reference — Delhi was the reference point; the stones showed her changing position.
4. Relative rest — Bus passengers seem at rest when the bus itself is the reference point.
5. Relative motion — The same passengers are in motion compared with outside objects like buildings.
Conclusion: Rest and motion are relative; they depend upon the reference point we choose.

Introduction: Curves and long road distances need special measurement methods beyond a straight scale.
Key Points:
1. Thread method — Place a thread along the curve, mark its ends, and straighten it.
2. Measure the thread — Measure the straightened thread's length using a metre scale.
3. Bicycle setup — Fix a flexible metal strip on a spoke so it hits the frame with a sound.
4. Counting turns — Each sound marks one wheel turn; count the sounds while riding slowly.
5. Finding distance — Multiply the wheel's outer boundary length by the number of turns.
Conclusion: Threads measure curves, and the bicycle method measures distances, like the Jones Counter.

Introduction: India has a rich history of measurement systems dating back to ancient times.
Key Points:
1. Ancient units — Angula (finger width), dhanusa and yojana appear in ancient Indian literature.
2. Their uses — These units measured artefacts, architecture and town planning in ancient India.
3. Angula today — Angula is still used by traditional craftspeople like carpenters and tailors.
4. Harappan scales — Objects with ruled markings, possibly scales, were excavated from Harappan sites.
5. Move to standard units — Different regional systems confused travellers, leading to worldwide SI units.
Conclusion: Ancient Indian units show our measurement heritage; standard units solved global confusion.

Introduction: The chapter gives clear rules for writing unit names and symbols of length correctly.
Key Points:
1. Unit names lowercase — Names like metre and centimetre begin with lowercase letters, except at sentence starts.
2. Symbols lowercase — Symbols km, m, cm and mm are always written in lowercase letters.
3. No plural 's' — Symbols never take 's' for plural; we write 10 km, never 10 kms.
4. No full stop — No full stop is written after a symbol, except at a sentence's end.
5. Space between — Always leave a space between the number and unit, like 7 m.
Conclusion: Following these rules, 'The length is 7 m' is written correctly and scientifically.

Introduction: Different measuring devices suit different lengths and shapes of objects.
Key Points:
1. Metre scale — A one-metre-long scale used for longer lengths, like measuring a room's height.
2. 15-cm scale — A small scale ideal for small objects, like measuring a pencil's length.
3. Flexible measuring tape — A bendable tape used for curved lengths and girths.
4. Girth measurement — A tree's girth or a person's chest size needs a flexible tape only.
5. Choosing correctly — The object's size and shape decide which device is most appropriate.
Conclusion: Using the right device gives accurate measurements for every situation.

Introduction: A children's park shows all three types of motion in its rides.
Key Points:
1. Linear motion — A child sliding down a slide moves along a straight line.
2. Circular motion — Children on a merry-go-round move along a circular path.
3. Oscillatory motion — A swing moves to and fro about its fixed resting position.
4. Eraser activity — Tie an eraser to a thread's end and hold the other end steadily.
5. Observation — Pull the eraser slightly to one side and release; it moves to and fro like a swing.
Conclusion: The hanging eraser demonstrates oscillatory motion exactly like a park swing.

Introduction: This question applies unit conversions and explains why standard units matter.
Key Points:
1. Convert to centimetres — 1.8 m = 1.8 × 100 cm = 180 cm.
2. Convert to millimetres — 180 cm = 180 × 10 mm = 1800 mm.
3. Handspan problem — Handspans differ in size, so another student gets a different number.
4. Why numbers differ — The unit size differs though the table's actual length stays the same.
5. Standard units preferred — Standard units give consistent, reliable measurements for everyone everywhere.
Conclusion: 1.8 m equals 180 cm or 1800 mm, and standard units avoid all handspan confusion.