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These are complete exercise solutions for Samacheer Kalvi 9th Science Chapter 1 — Measurement. Solve each question yourself first, then verify your method and answer below. Show all steps in numerical problems. Pay close attention to units and zero-error corrections, as these are the most commonly tested details in exams.
Key Concepts (Quick Recap)
| Term | Definition |
|---|
| Measurement | Comparison of a physical quantity with a known standard unit of the same nature |
| SI System | Système International d'Unités — 7 base units: metre, kilogram, second, kelvin, ampere, mole, candela |
| Vernier Caliper | Instrument to measure external diameter, internal diameter, and depth; LC = 1 MSD − 1 VSD = 0.01 cm |
| Screw Gauge | Instrument to measure thickness of thin objects; LC = pitch / no. of head scale divisions = 0.01 mm |
| Mass | Amount of matter in a body; scalar quantity; SI unit kilogram (kg); constant everywhere |
| Weight | Gravitational force acting on a body; vector quantity; SI unit newton (N); W = mg; varies with g |
| Temperature Scales | Celsius (°C), Fahrenheit (°F), Kelvin (K); K = °C + 273.15; F = (9/5)C + 32 |
| Light Year | Distance light travels in one year = 9.46 × 10¹⁵ m; used for astronomical distances |
| Least Count | Smallest measurement that can be accurately read with an instrument |
| Pitch of Screw Gauge | Distance moved by the screw per one complete rotation of the thimble |
| Zero Error | Error arising when the zero of the head/vernier scale does not coincide with the reference line at null position |
| Metric Ton | Unit of mass equal to 1000 kg or 10 quintals |
| Quintal | Unit of mass equal to 100 kg |
| Derived Unit | A unit formed by combining base units (e.g., newton = kg·m/s²) |
I. Choose the Best Answer
Q1. Which of the following is the correct ordering? (a) mm < cm < m < km ✓ (b) m < mm < cm < km (c) km < m < cm < mm (d) mm < m < cm < km
Answer(a) ✓ — mm < cm < m < km is the correct ascending order of length units.
Q2. Rulers, measuring tapes and metre scales are used to measure: (a) mass (b) weight (c) time (d) length ✓
Answer(d) ✓ — These instruments measure length/distance.
Q3. 1 metric ton is equal to: (a) 100 kg (b) 10 quintals ✓ (c) 10 kg (d) 1000 g
Answer(b) ✓ — 1 metric ton = 1000 kg = 10 quintals (1 quintal = 100 kg).
Q4. Which of the following is not a device to measure mass? (a) Spring balance ✓ (b) Beam balance (c) Physical balance (d) Digital balance
Answer(a) ✓ — A spring balance measures weight (force), not mass.
Q5. The least count of a screw gauge whose pitch is 1 mm and has 100 divisions on the head scale is: (a) 0.01 cm (b) 0.001 mm (c) 0.01 mm ✓ (d) 0.1 mm
Answer(c) ✓ — LC = Pitch / No. of head scale divisions = 1 mm / 100 = 0.01 mm.
Q6. Which of the following is a derived unit? (a) kilogram (b) metre (c) second (d) newton ✓
Answer(d) ✓ — Newton (N) = kg·m/s² is derived from base units; the others are base units.
Q7. The temperature 37°C in Kelvin is: (a) 310.15 K ✓ (b) 273.15 K (c) 37 K (d) 310 K
Answer(a) ✓ — K = °C + 273.15 = 37 + 273.15 = 310.15 K. Option (d) 310 K is a rounded approximation but (a) is exact.
Q8. Which instrument is used to measure the internal diameter of a pipe? (a) Screw gauge (b) Vernier caliper ✓ (c) Beam balance (d) Metre scale
Answer(b) ✓ — The vernier caliper has internal jaws specifically designed to measure internal diameters.
II. Fill in the Blanks
1. Metre is the unit of Length. 2. 1 kg of rice is weighed by a Beam balance. 3. Thickness of a cricket ball is measured by Vernier Caliper. 4. Radius of a thin wire is measured by Screw Gauge. 5. A physical balance measures small differences in mass up to 1 mg (0.001 g). 6. The SI unit of electric current is the ampere (A). 7. The distance travelled by light in one year is called a light year. 8. 0°C = 273.15 K. 9. The amount of matter present in a body is called its mass.
III. True or False
1. "The SI unit of electric current is the kilogram"
AnswerFalse The SI unit of electric current is the ampere (A); kilogram is the SI unit of mass.
2. "Kilometre is one of the SI units of measurement"
AnswerFalse Only metre (m) is the SI unit of length; kilometre is a derived multiple, not an SI base unit.
3. "In everyday life, we use the term weight instead of mass"
AnswerTrue Colloquially, "weight" is used when we actually mean mass (e.g., "my weight is 60 kg" actually refers to mass).
4. "A physical balance is more sensitive than a beam balance"
AnswerTrue A physical balance can measure to 1 mg; a beam balance measures to about 1 g.
5. "One Celsius degree is an interval of 1 K and zero degree Celsius is 273.15 K" → False (partially). The statement about the interval is correct (1°C interval = 1 K interval), but 0°C = 273.15 K, not 273 K exactly.
6. "Vernier caliper has an accuracy of 0.1 mm and screw gauge has accuracy of 0.01 mm"
AnswerFalse Vernier caliper accuracy = 0.01 cm = 0.1 mm; screw gauge accuracy = 0.01 mm. The values are stated correctly, but the phrasing suggests they are similar — screw gauge is 10 times more precise.
7. "Mass of a body changes from place to place"
AnswerFalse Mass is a scalar quantity that remains constant everywhere. It is weight (W = mg) that varies with the local value of g.
8. "A light year is a unit of time"
AnswerFalse A light year is a unit of distance — the distance light travels in one year (9.46 × 10¹⁵ m), not a unit of time.
IV. Match the Following
Set 1 — Physical quantities and SI units
| Column I | Column II |
|---|
| (a) Length | (ii) metre ✓ |
| (b) Mass | (iii) Kilogram ✓ |
| (c) Time | (iv) second ✓ |
| (d) Temperature | (i) Kelvin ✓ |
Set 2 — Instruments and their uses
| Column I | Column II |
|---|
| (a) Screw gauge | (ii) Coins ✓ |
| (b) Vernier Caliper | (iv) Cricket ball ✓ |
| (c) Beam balance | (i) Vegetables ✓ |
| (d) Digital balance | (iii) Gold ornaments ✓ |
V. Assertion and Reason
Q1. A: "The mass of the bag is 10 kg" is scientifically correct. R: In everyday life, we use the term weight instead of mass. → (a) Both A and R are true, but R is not the correct explanation for A. Mass is the correct scientific term; "weight" usage is colloquial, not the reason A is correct.
Q2. A: 0°C = 273.16 K. R: To convert Celsius to Kelvin, add 273.15. → (b) Both A and R are true and R is the correct reason. (0°C ≈ 273.15 K, but rounding gives 273 K in common use.)
Q3. A: Distance between celestial bodies is measured in light-years. R: One light-year is the distance light travels in one year. → (a) Both A and R are true and R is the correct explanation.
VI. Answer Briefly (2-mark)
Q1. Define measurement.
Answer
Measurement is the process of comparing a given physical quantity with a known standard quantity of the same nature, called a unit. It gives a numerical value along with a unit that expresses how many times the standard quantity is contained in the given quantity. For example, measuring the length of a table as 2 m means the table is 2 times the standard metre.
Q2. Define standard unit.
Answer
A standard unit is a fixed, universally accepted quantity of constant magnitude used as a reference for measuring physical quantities of the same kind. It must be easily reproducible, internationally accepted, and invariant over time and location. The SI system defines such standard units for all physical quantities.
Q3. What is the full form of the SI system?
Answer
SI stands for Système International d'Unités (International System of Units). It was adopted by the General Conference on Weights and Measures in 1960 to provide a uniform, worldwide system of measurement. The SI system is built on seven base units that cover all fundamental physical quantities.
Q4. What is least count?
Answer
The least count is the smallest measurement that can be accurately read with an instrument. It represents the instrument's precision. For a vernier caliper, LC = 1 MSD − 1 VSD. For a screw gauge, LC = Pitch / Number of head scale divisions. The smaller the least count, the more precise the instrument.
Q5. What is the pitch of a screw gauge?
Answer
Pitch is the distance moved by the screw along the pitch scale for one complete rotation of the thimble. It equals the distance between two successive threads on the screw. Typically, the pitch of a standard screw gauge is 0.5 mm or 1 mm. Knowing the pitch is essential for calculating the least count.
Q6. How do you find the diameter of a thin wire using a ruler?
Answer
Wind the wire tightly around a cylinder (e.g., a pencil) for a known length (say 10 cm), count the number of turns, then divide the total length by the number of turns to get the average diameter. For example, if 50 turns cover 10 cm, the diameter = 100 mm / 50 = 2 mm. This method gives only an approximate value.
Q7. What are the rules for writing SI unit symbols?
Answer
1. Units named after scientists are written in lowercase in full (newton, joule, kelvin) but their symbols are uppercase (N, J, K). 2. Symbols are never pluralised (100 kg, not 100 kgs). 3. No full stop after symbols unless at the end of a sentence (75 cm, not 75 cm.). 4. Symbols are always lowercase unless derived from a person's name (m for metre, N for newton).
Q8. Why do we need standard units of measurement?
Answer
Ancient measurement systems (hand span, foot, cubit) varied from person to person and place to place, causing confusion and inaccuracy in trade and science. After World War II, the need for a worldwide uniform system led to the SI system, recommended by the General Conference on Weights and Measures in 1960. Standard units ensure consistency, reproducibility, and universal understanding in all fields of science and commerce.
Q9. What are the differences between mass and weight?
Answer
| Property | Mass | Weight |
|---|
| Definition | Amount of matter in a body | Force of gravity on a body |
| Quantity type | Fundamental / Scalar | Derived / Vector |
| SI unit | kilogram (kg) | newton (N) |
| Instrument | Physical / Beam balance | Spring balance |
| Variation | Constant everywhere | Varies with g (location) |
| Formula | — | W = mg |
Q10. What is the least count of a vernier caliper?
Answer
Least count = 1 Main Scale Division − 1 Vernier Scale Division = 1 mm − 0.9 mm = 0.1 mm = 0.01 cm. It is the minimum length that can be measured accurately with the instrument. A vernier caliper with N vernier divisions has LC = (1 MSD) / N.
VII. Answer in Detail (5-mark)
Q1. Describe how you would measure the thickness of a hollow teacup using a screw gauge.
Answer
A screw gauge measures small thicknesses with high precision using the principle of a screw rotating through a nut. The procedure for measuring the wall thickness of a hollow teacup is as follows:
1. Determine the pitch: Rotate the thimble one full turn and observe the distance moved on the pitch scale. This distance per rotation is the pitch (typically 0.5 mm or 1 mm). 2. Calculate the least count: LC = Pitch / Number of head scale divisions. For a pitch of 0.5 mm and 50 divisions: LC = 0.5 / 50 = 0.01 mm. 3. Check for zero error: Bring the studs into contact. If the zero of the head scale aligns with the pitch scale baseline, there is no zero error. If it does not align, note the zero correction (positive or negative). 4. Place the teacup wall between the anvil and spindle. The wall should rest flat against the anvil. 5. Rotate the thimble using the ratchet until the teacup is held firmly — do not over-tighten, as this can deform the object. 6. Note the readings: Record the Pitch Scale Reading (PSR) and Head Scale Coincidence (HSC). 7. Calculate the thickness: Thickness = PSR + (HSC × LC) ± zero correction. 8. Repeat at different positions on the wall, tabulate the readings, and find the average thickness for greater accuracy.
Always record readings in a table with columns for PSR, HSC, observed reading, corrected reading, and average.
Q2. Describe how you would measure the thickness of a one-rupee coin using a screw gauge.
Answer
The procedure is the same as measuring any thin object with a screw gauge:
1. Determine the pitch and least count: For a standard screw gauge, pitch = 0.5 mm or 1 mm. LC = Pitch / Number of head scale divisions. A typical screw gauge has LC = 0.01 mm. 2. Check for zero error: Close the studs and check alignment. If the zero of the circular scale is below the reference line, the zero error is positive; if above, it is negative. Record the zero correction accordingly. 3. Place the coin between the anvil and spindle. Ensure the coin sits flat and is not tilted. 4. Use the ratchet to hold the coin firmly. Stop turning when the ratchet clicks — this ensures consistent pressure. 5. Note PSR and HSC. The PSR is read from the pitch scale at the edge of the thimble; HSC is the head scale division that aligns with the pitch scale reference line. 6. Calculate: Total reading = PSR + (HSC × LC) ± zero correction. 7. Repeat at different positions on the coin (centre, edge, and at least two more points) and calculate the average thickness.
For example, if PSR = 1 mm, HSC = 68, LC = 0.01 mm, and no zero error: Thickness = 1 + (68 × 0.01) = 1.68 mm.
VIII. Numerical Problems
Q1. Inian says the value of 1 light-year is 9.46 × 10¹⁵ m, while Ezhilan says it is 9.46 × 10¹² km. Who is correct?
Answer
Both are correct. 1 light-year = 9.46 × 10¹⁵ m. Since 1 km = 10³ m, Ezhilan's value: 9.46 × 10¹² km = 9.46 × 10¹² × 10³ m = 9.46 × 10¹⁵ m. Both values match. ✓
Q2. Vernier caliper measurement — rubber ball radius:
Answer
- Main Scale Reading (MSR) = 7 cm
- Vernier Coincidence (VC) = 6
- Least Count (LC) = 0.01 cm
Radius = MSR + (VC × LC) = 7 + (6 × 0.01) = 7 + 0.06 = 7.06 cm
Q3. Screw gauge measurement — five-rupee coin thickness:
Answer
- Pitch Scale Reading (PSR) = 1 mm
- Head Scale Coincidence (HSC) = 68
- Least Count (LC) = 0.01 mm
Thickness = PSR + (HSC × LC) = 1 + (68 × 0.01) = 1 + 0.68 = 1.68 mm
Common Mistakes to Avoid
1. ❌ Using "weight" when you mean "mass" → ✅ Mass (kg) is constant; weight (N) changes with gravity. Never write "weight = 60 kg" — it should be "mass = 60 kg."
2. ❌ Writing vernier caliper LC as 0.01 mm → ✅ Vernier caliper LC = 0.01 cm = 0.1 mm. Screw gauge LC = 0.01 mm. The screw gauge is 10 times more precise.
3. ❌ Skipping zero error correction → ✅ Always check and apply zero error before calculating final readings. A positive zero error is subtracted; a negative one is added.
4. ❌ Mixing PSR/MSR units without conversion → ✅ Pitch scale is in mm for screw gauge; main scale is in mm or cm for vernier caliper. Always convert to the same units before adding.
5. ❌ Writing "kgs" or "cms" as SI symbols → ✅ SI symbols are never pluralised. Write "100 kg" not "100 kgs." Kelvin symbol is uppercase K; kilo prefix is lowercase k.
6. ❌ Converting °C to K by adding 273 → ✅ K = °C + 273.15. The interval sizes are equal (1°C change = 1 K change), but the zero points differ by 273.15.
7. ❌ Saying spring balance measures mass → ✅ Spring balance measures weight (force). Beam balance and physical balance measure mass by comparing with standard masses.
Exam Checklist
- [ ] SI base units and their symbols memorized (7 base quantities)
- [ ] Difference between mass and weight clearly understood (scalar vs vector, kg vs N)
- [ ] Vernier caliper: least count, zero error, reading procedure
- [ ] Screw gauge: pitch, least count, zero error, reading procedure
- [ ] Temperature conversions between °C, °F, K practised
- [ ] Light-year definition and numerical value (9.46 × 10¹⁵ m)
- [ ] Assertion-Reason question technique practised
- [ ] Numerical problems on vernier caliper and screw gauge practised
- [ ] Rules for writing SI unit symbols (no plurals, correct case)
- [ ] Metric ton and quintal conversion (1 ton = 10 quintals = 1000 kg)
- [ ] Difference between fundamental and derived units with examples
- [ ] Procedure for measuring thickness of coin and teacup wall with screw gauge
Internal Links
- [Chapter 1 Guide — Measurement](/school/tamil-nadu-state-board/class/9/science/measurement)
- [All Class 9 Science Solutions](/school/tamil-nadu-state-board/class/9/science/solutions)
- [Class 9 Science Subject Guide](/school/tamil-nadu-state-board/class/9/science)
