6. Measurement of Physical Quantities

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Chapter 6 – Measurement of Physical Quantities (Class 7)

Chapter 6: Measurement of Physical Quantities

Class 7 • Maharashtra Board General Science Mobile-friendly • Neat & Colourful • Proper line gaps

1) 20 Important Words & Meanings (Meanings in Hindi)

Physical quantityऐसी मापने योग्य चीज़ जिसका मान और इकाई हो (जैसे लंबाई, द्रव्यमान, समय)।
Magnitudeकिसी राशि का संख्यात्मक मान (कितना)।
Unitमाप की तय मानक मात्रा (जैसे मीटर, किलोग्राम, सेकंड)।
Scalarजिसे केवल मान से ही पूरी तरह बताया जा सके (दिशा नहीं)।
Vectorजिसे मान के साथ दिशा बताकर ही पूरा बताया जा सके।
Massकिसी वस्तु में पदार्थ की मात्रा (द्रव्यमान)।
Weightगुरुत्वाकर्षण के कारण वस्तु पर लगने वाला बल (भार)।
Inertiaवस्तु की स्थिति बदलने के विरोध की प्रवृत्ति (जड़त्व)।
Speedकितनी तेज़ी से दूरी तय हुई — दूरी/समय।
Velocityदिशा सहित गति — गति + दिशा।
Densityद्रव्यमान/आयतन — पदार्थ कितना सघन है।
Standardizationमाप-तौल के औज़ारों को तय मानक से मिलाना/जांचना।
MKS systemमीटर-किलोग्राम-सेकंड आधारित मापन पद्धति।
CGS systemसेंटीमीटर-ग्राम-सेकंड आधारित मापन पद्धति।
SI unitsअंतरराष्ट्रीय मानक इकाइयां (मीटर, किलोग्राम, सेकंड आदि)।
Parallax errorस्केल को तिरछा/गलत कोण से देखने पर होने वाली गलती।
Least countकिसी उपकरण की सबसे छोटी माप-क्षमता।
Precisionमाप की सूक्ष्मता/दोहराव-योग्यता।
Accuracyवास्तविक मान के कितने पास माप है (शुद्धता)।
TMCथाउज़ेंड मिलियन क्यूबिक फीट — बाँध की जल-क्षमता की इकाई।

2) Important Notes (Quick Revision)

  • Physical quantities are described by a value and a unit. Example: “2 kilometre” — value = 2, unit = km.
  • Scalars (length, time, mass, temperature, area, work) need only magnitude; vectors (displacement, velocity) need magnitude and direction.
  • Mass (scalar) measures matter & inertia; same everywhere. Weight (vector) is gravitational force: \(W = m\,g\); varies with \(g\).
  • Why weight varies? \(g\) is a bit larger at poles, smaller at equator/altitude ⇒ weight changes; mass does not.
  • Standard units avoid confusion from body-based measures (hand-span, cubit). Use SI units: metre (m), kilogram (kg), second (s).
QuantitySI (MKS)CGSCommon units (context)
Lengthmetre (m)centimetre (cm)kilometre (km)
Masskilogram (kg)gram (g)tonne, milligram
Timesecond (s)second (s)minute, hour
Speedm/scm/skm/h
Aream\(^{2}\)cm\(^{2}\)hectare
Volumem\(^{3}\)cm\(^{3}\)litre (L) for liquids
Densitykg/m\(^{3}\)g/cm\(^{3}\)—

Key formulas

Speed: \(v=\dfrac{d}{t}\),   Area (rectangle): \(A=\ell\times b\),   Volume (cuboid): \(V=\ell\times b\times h\).

Weight: \(W=m\,g\) (vector),   Density: \(\\rho=\dfrac{m}{V}\).

  • TMC & conversions: \(1\ \text{cubic foot}=28.317\ \text{L}\). \(1\ \text{TMC} = 10^9\ \text{ft}^3 = 28{,}316{,}846{,}592\ \text{L} \approx 28.317\ \text{billion L}\).
  • Accurate measurement needs the right device, correct use (eye at scale level to avoid parallax), zero check, stable placement, and standardization (Legal Metrology/Weights & Measures).

3) 20 Important “One-Word Answer” Type Questions

  1. Quantity described by a value and a unit is called?
    Physical quantity.
  2. A quantity needing only magnitude?
    Scalar.
  3. A quantity needing magnitude and direction?
    Vector.
  4. SI unit of length?
    Metre (m).
  5. SI unit of mass?
    Kilogram (kg).
  6. SI unit of time?
    Second (s).
  7. Relation for speed?
    \(v=\dfrac{d}{t}\).
  8. Measure proportional to inertia?
    Mass.
  9. Earth’s gravitational pull on a mass is?
    Weight.
  10. At which place is weight maximum: poles or equator?
    Poles (slightly higher \(g\)).
  11. Common balance compares?
    Masses.
  12. Unit of area in SI?
    Square metre (m\(^{2}\)).
  13. Unit of volume (solid) in SI?
    Cubic metre (m\(^{3}\)).
  14. Unit of density in SI?
    kg/m\(^{3}\).
  15. Unit of velocity in SI?
    m/s.
  16. MKS expands to?
    Metre–Kilogram–Second.
  17. CGS expands to?
    Centimetre–Gram–Second.
  18. Standard metre prototype was kept in?
    International Bureau of Weights and Measures (Paris).
  19. What does standardization ensure?
    Accuracy and fairness in trade measurements.
  20. 1 cubic foot equals how many litres (approx.)?
    28.317 L.

4) 20 Very Short Answer Questions (1–2 lines)

  1. Why do we need standard units?
    Body-based units vary from person to person; standards give uniform, comparable results.
  2. Why is mass the same on Moon?
    Mass is amount of matter; it doesn’t depend on gravity.
  3. Why is weight less at high altitude?
    \(g\) decreases slightly with height, so \(W=m g\) is smaller.
  4. Give two scalar quantities.
    Temperature, time (also mass, length).
  5. Give two vector quantities.
    Displacement, velocity.
  6. What is parallax error?
    Reading a scale from an angle; avoid by keeping eye perpendicular to the scale.
  7. State SI base units used here.
    Metre (m), kilogram (kg), second (s).
  8. Formula for density.
    \(\\rho=\dfrac{m}{V}\).
  9. If \(d=100\,\text{km}\) and \(t=2\,\text{h}\), speed?
    \(v=50\,\text{km h}^{-1}\).
  10. Name the department that checks shop balances.
    Weights & Measures (Legal Metrology) sub-division.
  11. Two checks before buying by weight.
    Standardization stamp; pointer at zero/upright; stable balance.
  12. What is least count?
    Smallest measurement a device can reliably read.
  13. Unit for liquid volume commonly used.
    Litre (L).
  14. Which changes more with latitude—mass or weight?
    Weight.
  15. Area needed to find classroom floor?
    Length × breadth → area in m\(^{2}\).
  16. Why is accurate measurement essential in sports timing?
    Tiny time differences decide winners; needs high precision devices.
  17. Speed vs velocity?
    Speed has no direction; velocity has direction.
  18. 1 TMC equals roughly how many litres?
    \(28{,}316{,}846{,}592\) L (≈ 28.317 billion L).
  19. What is standardization?
    Checking/adjusting instruments against accepted standards at intervals.
  20. Give one cause of measurement error.
    Wrong instrument selection or improper use.

5) 20 Short Answer Questions (2–3 lines)

  1. Differentiate mass and weight.
    Mass is the amount of matter (scalar, constant). Weight is gravitational force \(W=m g\) (vector), varies with \(g\).
  2. Why is weight maximum at poles?
    Earth’s radius is slightly smaller at poles and rotation effect is minimum → effective \(g\) is a bit larger.
  3. Why shouldn’t we use hand-span as a unit?
    Hand-spans differ among people and even for the same person over time; leads to inconsistent results.
  4. State two precautions for accurate measurement.
    Choose proper device & range; avoid parallax by eye-level reading; zero/check calibration before use.
  5. Explain speed formula with units.
    \(v=\dfrac{d}{t}\). If \(d\) in metres and \(t\) in seconds, \(v\) is in m/s; if km and h, then km/h.
  6. How do we compute classroom area?
    Measure length \((\ell)\) and breadth \((b)\) with a metre scale; \(A=\ell\times b\) in m\(^{2}\).
  7. Why check balance pointer at zero?
    A shifted zero gives systematic error in every reading; zeroing removes this bias.
  8. Give two market checks for fairness.
    Standardization seal on weights & balance; intact pans/underside, stable support and no tampering.
  9. What is density and how is it measured?
    Density is mass per unit volume: \(\\rho=\dfrac{m}{V}\). SI unit kg/m\(^{3}\); use balance and measuring cylinder.
  10. Distinguish MKS and CGS.
    MKS uses metre–kilogram–second; CGS uses centimetre–gram–second; same physics, different unit sizes.
  11. Why do we standardize petrol pumps?
    To ensure the indicated litres equal actual volume delivered; protects consumers.
  12. Give two examples of vectors from this chapter.
    Displacement and velocity (both need direction).
  13. Give two examples of scalars from this chapter.
    Mass and temperature (no direction needed).
  14. How does altitude affect \(g\)?
    As altitude increases, distance from Earth’s centre increases → \(g\) decreases slightly.
  15. Convert \(120\,\text{km}\) in \(2.5\,\text{h}\) to speed.
    \(v=\dfrac{120}{2.5}=48\,\text{km h}^{-1}\).
  16. Why is litre used for liquids though SI volume is m\(^{3}\)?
    Litre is convenient for everyday liquid volumes (1 L = 1000 cm\(^{3}\) = 0.001 m\(^{3}\)).
  17. State two major causes of errors in measurement.
    Wrong device/least count; improper technique (parallax, zero error, unstable setup).
  18. What does precision mean?
    How finely and consistently an instrument reads (repeatability), even if not exactly accurate.
  19. What does accuracy mean?
    Closeness of a reading to the true value; improved by calibration and proper method.
  20. Explain why velocity is a vector but speed is scalar.
    Velocity includes direction (e.g., 10 m/s north); speed gives only magnitude (10 m/s).

6) Textbook Exercise – Perfect Answers

Q1) Write answers in your own words.
  1. (a) Why is the weight of the same object different on different planets?
    Weight is \(W=m\,g\). Different planets have different gravitational acceleration \(g\) (due to mass and radius), so for the same mass \(m\), \(W\) changes.
  2. (b) What precautions will you take to make accurate measurements in day-to-day affairs?
    Use the correct instrument and range; check zero/calibration; read at eye level to avoid parallax; keep device stable; use standard units; note least count; repeat and average if needed.
  3. (c) What is the difference between mass and weight?
    Mass is the amount of matter (scalar, constant everywhere). Weight is gravitational force \(W=m g\) (vector) and varies with location where \(g\) differs.
Q2) Who is my companion? (Match the pairs)
Group ‘A’Correct companion in Group ‘B’
Velocitymetre/second (m/s)
Areasquare metre (m\(^{2}\))
Volumelitre (L) (for liquids) / cubic metre (m\(^{3}\))
Masskilogram (kg)
Densitykilogram/cubic metre (kg/m\(^{3}\))
Q3) Explain giving examples: (a) Scalar quantity (b) Vector quantity
  1. (a) Scalar
    Defined completely by magnitude: e.g., time = 5 s, mass = 2 kg, temperature = \(37^\circ\text{C}\).
  2. (b) Vector
    Needs magnitude and direction: e.g., displacement = 3 km east; velocity = 20 m/s north.
Q4) Explain, giving examples, the errors that occur while making measurements.

Using wrong device/least count (measuring millimetres with a rough ruler), improper use (parallax, not zeroing), unstable support (vibrations), worn/tampered weights, temperature effects. Example: reading a thermometer not at eye level gives parallax error.

Q5) Give reasons.
  1. (a) It is not proper to measure quantities by using body parts as units.
    Body parts vary from person to person and even for the same person over time, giving inconsistent results; hence not standard.
  2. (b) It is necessary to get the weights and measures standardized at regular intervals.
    Instruments can drift, wear out, or be tampered with. Periodic standardization ensures accuracy, legality and fairness in trade.
Q6) Explain the need for accurate measurement and the devices to be used for that.

Accurate measurement is essential in health (thermometers), commerce (balances, fuel dispensers), sports timing, engineering, and science. Use appropriate devices with suitable least count—measuring tape/metre rule for length, calibrated balances for mass, stopwatches/chronographs for time, volumetric flasks/cylinders for volume—and follow correct technique and standardization.

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