Measurement and Experimentation Class 9 ICSE — Physics Ch 1
Measurement and Experimentation Class 9 ICSE is Chapter 1 of the Physics textbook. It lays out the ideas every lab experiment depends on. Measurement and the unit come first, then the S.I. system of units. The chapter moves from units of length and time to the instruments that measure them — the vernier callipers, the screw gauge and the simple pendulum — with their formulas and correction rules.
ICSE Class 9 Physics Chapter 1 Measurements and Experimentation PDF
What is inside Chapter 1
25 pages · 13 sections · 4 worked examples · 91 exercise questions
| Section | Title |
|---|---|
| 1.1 | NEED OF UNIT FOR MEASUREMENT |
| 1.2 | SYSTEMS OF UNIT |
| 1.3 | UNITS OF LENGTH |
| 1.5 | UNITS OF TIME |
| 1.6 | SOME EXAMPLES OF DERIVED UNITS |
| 1.7 | GUIDELINES FOR WRITING THE UNITS |
| 1.8 | LEAST COUNT OF A MEASURING INSTRUMENT |
| 1.9 | MEASUREMENT OF LENGTH |
| 1.10 | PRINCIPLE OF VERNIER |
| 1.11 | VERNIER CALLIPERS |
| 1.12 | PRINCIPLE OF A SCREW |
| 1.13 | SCREW GAUGE |
| 1.14 | MEASUREMENT OF TIME |
- EXERCISE 1(A): 26 questions
- Multiple choice type :: 11 questions
- EXERCISE 1 (B): 25 questions
- Multiple choice type :: 17 questions
- Multiple choice type :: 12 questions
1.1 Need of Unit for Measurement
Measurement begins with comparison. To measure a physical quantity, you take a constant quantity of the same nature as a standard and count how many times it fits into the given quantity. Measurement is the process of comparing a physical quantity with a known standard quantity of the same nature. That standard quantity is the unit.
Every measurement has two parts: the unit and the number that says how many times that unit is contained. The magnitude is therefore written as a number times a unit:
\text{Physical quantity} = \text{numerical value} \times \text{unit}Take a sack of rice marked 40 kg. The kilogram is the unit, and it fits 40 times into the mass of the rice. Change the unit to grams and the number becomes 40,000, but the quantity stays the same.
A good unit has four qualities. It should be of convenient size. It must be definable without ambiguity. It must be reproducible, and its value must not change with space or time. The last three conditions are essential for international acceptance.
Units are of two kinds. Fundamental units are independent — metre, kilogram and second cannot be built from any other unit. Derived units are expressed in terms of fundamental units. Area, for example, is \text{length} \times \text{length}, so its unit is \text{m}^2.
1.2 Systems of Unit
Before the S.I. system, three systems governed mechanics. The C.G.S. system used centimetre, gram and second. The F.P.S. system used foot, pound and second. The M.K.S. system used metre, kilogram and second. All three are now of historical importance only.
In 1960, the General Conference of Weights and Measures enlarged the metric system. The result is the S.I. system (Système Internationale d’Unités), with seven fundamental units and two complementary units — the radian for angle and the steradian for solid angle.
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Luminous intensity | candela | cd |
| Electric current | ampere | A |
| Amount of substance | mole | mol |
| Angle | radian | rad |
| Solid angle | steradian | sr |
For very large or very small measurements, a prefix is attached to the unit. Large values use deca 10^1, hecto 10^2, kilo 10^3, mega 10^6, giga 10^9, tera 10^{12}, peta 10^{15}, exa 10^{18}, zetta 10^{21} and yotta 10^{24}.
Small values use deci 10^{-1}, centi 10^{-2}, milli 10^{-3}, micro 10^{-6}, nano 10^{-9}, pico 10^{-12}, femto 10^{-15}, atto 10^{-18}, zepto 10^{-21} and yocto 10^{-24}. To keep their order, try the mnemonic: Daring Cats Make Microbes Nervous — Pouncing Fast At Zealous Yaks.
To read a prefix in a question, replace it with its power of ten. 3.0 MHz means 3.0 \times 10^6\ \text{Hz}. 250 ps means 250 \times 10^{-12}\ \text{s}, which is 2.5 \times 10^{-10}\ \text{s}.
1.3 Units of Length
The S.I. unit of length is the metre (m). Its definition changed three times. In 1889, it was the distance between two marks on a platinum-iridium bar kept at 0°C. In 1960, it became 1,650,763.73 wavelengths of a krypton-86 spectral line. Since 1983, one metre is the distance light travels in \frac{1}{299,792,458} of a second.
| Smaller unit | Value in metre | Bigger unit | Value in metre |
|---|---|---|---|
| cm | 10^{-2} | km | 10^{3} |
| mm | 10^{-3} | A.U. | 1.496 \times 10^{11} |
| micron (μ) | 10^{-6} | light year | 9.46 \times 10^{15} |
| nm | 10^{-9} | parsec | 3.08 \times 10^{16} |
| Å | 10^{-10} | ||
| fermi (f) | 10^{-15} |
A light year measures distance, not time. It is the distance light travels in vacuum in one year. The astronomical unit (A.U.) is the mean distance between the earth and the sun. The parsec is the distance from which one A.U. subtends an angle of one second of arc.
Conversion pattern: express 7200 Å in nanometres and metres. Since 1\ \text{nm} = 10\ \text{Å}, 7200\ \text{Å} = 720\ \text{nm}. Since 1\ \text{Å} = 10^{-10}\ \text{m}, 7200 \times 10^{-10}\ \text{m} = 7.2 \times 10^{-7}\ \text{m}.
Mass uses the same idea. The S.I. unit is the kilogram. Smaller units are gram 10^{-3}\ \text{kg} and milligram 10^{-6}\ \text{kg}. Bigger units are quintal (100 kg) and metric tonne (1000 kg, or 10 quintals). Atomic masses use 1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg}, one-twelfth the mass of a carbon-12 atom. Stars are weighed in solar masses: 1\ \text{solar mass} = 2 \times 10^{30}\ \text{kg}.
Conversion pattern: 3.5 metric tonnes = 3.5 \times 1000 = 3500\ \text{kg}, and 3500 \div 100 = 35 quintals.
1.5 Units of Time
The S.I. unit of time is the second (s), and its definition has changed twice. A second was first \frac{1}{86400} of a mean solar day. Because the solar day varies, 1956 fixed the year 1900 as the standard, making one second \frac{1}{31,556,925.9747} of that year. In 1964, the second became 9,192,631,770 vibrations of the cesium-133 atom.
Smaller units of time are millisecond 10^{-3}\ \text{s}, microsecond 10^{-6}\ \text{s}, shake 10^{-8}\ \text{s} and nanosecond 10^{-9}\ \text{s}.
The bigger units follow a fixed chain:
- minute = 60\ \text{s}
- hour = 3600\ \text{s}, day = 86{,}400\ \text{s}
- month \approx 2.592 \times 10^{6}\ \text{s}
- year = 3.1536 \times 10^{7}\ \text{s}
- decade = 3.1536 \times 10^{8}\ \text{s}
- century = 3.16 \times 10^{9}\ \text{s}
- millennium = 3.16 \times 10^{10}\ \text{s}
A year has 365 days, so a leap year of 366 days compensates for the extra 0.2422 days. Every year divisible by 4 is a leap year, except century years, which must be divisible by 400. That is why 2000 was a leap year but 2100 will not be.
Worked pattern: one leap year = 366 \times 86{,}400\ \text{s} = 3.162 \times 10^{7}\ \text{s}, slightly longer than an ordinary year. Calendars based on moon phases, such as the Hindu and Islamic calendars, use the lunar month of nearly 29.5 days.
1.6 Some Examples of Derived Units
Every unit that is not fundamental is a derived unit, built from the seven fundamental ones. The method is always the same: write the defining equation of the quantity, replace each quantity by its unit, then simplify the powers.
| Quantity | Derived unit (symbol) |
|---|---|
| Area | \text{m}^2 |
| Volume | \text{m}^3 |
| Density | \text{kg m}^{-3} |
| Speed or velocity | \text{m s}^{-1} |
| Acceleration | \text{m s}^{-2} |
| Force | \text{N} = \text{kg m s}^{-2} |
| Work or energy | \text{J} = \text{kg m}^2\text{ s}^{-2} |
| Power | \text{W} = \text{kg m}^2\text{ s}^{-3} |
| Pressure | \text{Pa} = \text{kg m}^{-1}\text{ s}^{-2} |
| Frequency | \text{Hz} = \text{s}^{-1} |
| Electric charge | \text{C} = \text{A s} |
Check the pattern yourself with pressure. Pressure is force divided by area. So its unit is \frac{\text{kg m s}^{-2}}{\text{m}^2} = \text{kg m}^{-1}\text{ s}^{-2}, which is the pascal. Learn the defining equation first; the unit then follows without memorising.
1.7 Guidelines for Writing the Units
These conventions decide whether an examiner can read your units correctly:
- Small letters for units not named after scientists: m, kg, s.
- Capitals for units named after scientists: N (newton), J (joule), W (watt), Pa (pascal), Hz (hertz), C (coulomb), V (volt).
- Full names start lowercase: newton, joule, watt — never Newton, Joule.
- Multiplication units use a dot, cross or space: N m, N·m or N × m.
- Division units use negative powers: \text{m s}^{-1}, not m/s in the final answer.
- No plural symbols: 10 m, never 10 ms, because ms means millisecond.
- Only one prefix per unit: write GW, not kMW.
- A prefix cubes with the unit: \text{km}^3 = (10^3\ \text{m})^3 = 10^9\ \text{m}^3, not 10^3\ \text{m}^3.
The last rule surprises most students. Because the prefix is part of the symbol, the power of ten is also cubed. This matters whenever volume or area is converted.
1.8 Least Count of a Measuring Instrument
The least count of an instrument is the smallest measurement that can be taken accurately with it. On a graduated scale, it is simply the value of one smallest division. Smaller the least count, more precise the measurement.
Three examples fix the idea:
- Metre rule: one division is 1 mm.
- Stopwatch: if 10 divisions sit between the 0 and 5 s marks, one division is 5 \div 10 = 0.5\ \text{s}.
- Ammeter: if 5 divisions sit between 0 and 1 A, one division is 1 \div 5 = 0.2\ \text{A}.
Check the principle with this question: which ammeter is more precise, one with 5 divisions between 0 and 1 A, or one with 10 divisions? The second has least count 0.1\ \text{A}, so it is more precise. This is why the vernier callipers and screw gauge exist — their least counts are smaller than 0.1 cm.
1.9 Measurement of Length
A metre rule has 10 subdivisions in each centimetre, so one small division is 1 mm, or 0.1 cm. That fixes its limit: a metre rule measures length correctly only up to 1 mm — one decimal place of a centimetre.
Suppose an object’s end falls between two millimetre marks. The rule forces you to take the nearer mark. The second decimal place of the centimetre then cannot be read at all.
Vernier callipers and screw gauge exist precisely because their least counts are smaller than 0.1 cm. The metre rule stays useful for everyday lengths, but finer instruments take over where its accuracy ends.
1.10 Principle of Vernier
Pierre Vernier found a way to read the second decimal place of a centimetre. His method uses two scales: a fixed main scale with 1 mm divisions, and a sliding vernier scale. On a standard vernier, 10 vernier divisions cover the same length as 9 main scale divisions — that is, 9 mm.
Each vernier division is therefore 0.9 mm, smaller than a main scale division by 0.1 mm. That difference is the least count. If n vernier divisions equal n − 1 main scale divisions, and one main scale division is x, then
\text{L.C.} = x - \frac{(n-1)x}{n} = \frac{x}{n}For the standard vernier, x = 1\ \text{mm} and n = 10, so \text{L.C.} = 0.1\ \text{mm} = 0.01\ \text{cm}.
The reading rule has two parts. First take the main scale reading: the mark just before the vernier zero. Then find the vernier division p that coincides exactly with any main scale division. The total reading is
\text{Total reading} = \text{main scale reading} + p \times \text{L.C.}Worked pattern with fresh numbers: least count 0.01 cm, vernier zero just past 2.7 cm, and the 6th division coincides. Reading = 2.7 + 6 \times 0.01 = 2.76\ \text{cm}.
Why does p \times \text{L.C.} give the gap between the marks? Because p vernier divisions cover p main scale divisions minus exactly that gap. Each coinciding division therefore contributes one least count to the missing length.
1.11 Vernier Callipers
A vernier callipers measures the length of a rod, the diameter of a sphere, the internal and external diameters of a hollow cylinder, and the depth of a beaker. Its parts have specific jobs:
| Part | Function |
|---|---|
| Outside jaws | Length of rod, diameter of sphere, external diameter of cylinder |
| Inside jaws | Internal diameter of a hollow cylinder or pipe |
| Strip | Depth of a beaker or bottle |
| Main scale | Reads length correct to 1 mm |
| Vernier scale | Reads length correct to 0.1 mm |
The least count is \text{L.C.} = \frac{x}{n}, where x is one main scale division and n is the number of vernier divisions. It can be reduced by increasing n or decreasing x.
Zero error appears when the two jaws touch but the vernier zero does not meet the main scale zero. If the vernier zero sits to the right, the error is positive; to the left, negative. The correction rule is always the same:
\text{Correct reading} = \text{observed reading} - \text{zero error (with sign)}Worked pattern: L.C. = 0.01 cm, zero error = +0.03 cm, main scale reading = 4.2 cm, p = 5. Observed reading = 4.2 + 5 \times 0.01 = 4.25\ \text{cm}. Correct reading = 4.25 - 0.03 = 4.22\ \text{cm}.
Zero error mistakes cost easy marks:
- Adding a positive zero error instead of subtracting it.
- Ignoring the sign of a negative error. A zero error of −0.04 cm is subtracted as \text{observed} - (-0.04) = \text{observed} + 0.04\ \text{cm}.
- Reading the wrong coinciding division — it must line up exactly with a main scale division.
1.12 Principle of a Screw
The pitch of a screw is the linear distance it moves along its axis in one complete rotation of its head. It equals the distance between two consecutive threads, usually 1 mm or 0.5 mm.
To measure small lengths, the head is made large and graduated around its circumference. This is the circular scale, normally divided into 50 or 100 parts. The least count of a screw is the distance moved along the axis when the circular scale turns by one division:
\text{L.C.} = \frac{\text{pitch}}{\text{number of divisions on the circular scale}}Worked pattern with new numbers: a screw moves 1 mm in two rotations, and its head has 100 divisions. Pitch = 1 \div 2 = 0.5\ \text{mm}. Least count = 0.5 \div 100 = 0.005\ \text{mm} = 0.0005\ \text{cm}.
The screw converts a tiny linear movement into a visible rotation of the head. One division of the circular scale then represents a known fraction of a millimetre. That is the whole principle.
1.13 Screw Gauge
A screw gauge works on the principle of a screw. It measures the diameter of a wire or the thickness of a paper correct to the third decimal place of a centimetre — 0.001 cm. A micrometer screw gauge reaches 1\ \mu = 0.0001\ \text{cm}.
| Part | Function |
|---|---|
| Ratchet | Turns the screw until the object is held gently |
| Sleeve | Carries the main scale and base line |
| Thimble | Carries the circular scale |
| Main scale | Reads length correct to 1 mm |
| Circular scale | Reads length correct to 0.01 mm |
The least count uses the same formula as the screw: \text{L.C.} = \frac{\text{pitch}}{\text{divisions on the circular scale}}.
Zero error works like the vernier. With the screw touching the stud, the circular scale zero should meet the base line. Zero below the line gives a positive error; zero above it gives a negative error. The correction is again: correct reading = observed reading − zero error (with sign).
Backlash error occurs when worn threads make the screw tip stay still for part of a reversed rotation. Rotate the ratchet in one direction only, and never reverse it suddenly.
Worked pattern: pitch = 1 mm, 100 divisions on the circular scale, main scale reading = 4 mm, p = 63, no zero error. L.C. = 0.01 mm. Diameter = 4 + 63 \times 0.01 = 4.63\ \text{mm} = 0.463\ \text{cm}.
The three length instruments form an accuracy ladder — lower least count means higher accuracy:
| Instrument | Least count | Typical use |
|---|---|---|
| Metre rule | 1 mm | Lengths like a pencil |
| Vernier callipers | 0.1 mm | Diameters of cylinders, depths |
| Screw gauge | 0.01 mm | Thickness of wire or paper |
1.14 Measurement of Time
A simple pendulum is a heavy point mass (the bob) suspended from a rigid support by a massless, inextensible string. This is an ideal case. In practice, a heavy ball hangs on a light thread. The clock pendulum is not simple — it is a compound pendulum.
Key terms:
- Oscillation: one complete to-and-fro motion of the bob.
- Time period T: time for one oscillation, measured in seconds.
- Frequency f: oscillations per second, f = \frac{1}{T}, in hertz.
- Amplitude: maximum displacement of the bob from its mean position.
- Effective length l: distance from the point of suspension to the centre of gravity of the bob.
The time period is given by
T = 2\pi\sqrt{\frac{l}{g}}where g is the acceleration due to gravity. To measure T, you time 20 oscillations with a stopwatch and divide: T = \frac{t}{20}. Timing many swings shrinks the stopwatch error.
If T^2 is plotted against l, the graph is a straight line through the origin of the data. Its slope is \frac{4\pi^2}{g}, so g = \frac{4\pi^2}{\text{slope}}.
Two dependencies matter: T \propto \sqrt{l} and T \propto \frac{1}{\sqrt{g}}. Mass of the bob and amplitude (for small swings) do not affect T. That is why a pendulum clock runs fast in winter — the metal contracts, l shortens, T drops — and slow in summer. On a swing, standing raises the centre of gravity, shortens l, and the swing moves faster.
Ratio pattern with new numbers: lengths 0.5 m and 2 m give \frac{T_1}{T_2} = \sqrt{\frac{0.5}{2}} = \frac{1}{2}. Gravity values 9.8 and 2.45\ \text{m s}^{-2} give the same 1 : 2 ratio.
A seconds’ pendulum has T = 2\ \text{s} and frequency 0.5 Hz. Its length is about 1 m where g = 9.8\ \text{m s}^{-2}.
For the ideas that build on these measurements, see the next chapter on motion in one dimension.
What to practise from this chapter
This table maps every question block in the chapter to the sections it tests:
| Block | Questions | Tests |
|---|---|---|
| Exercise 1(A) | 26 | Sections 1.1–1.7 |
| Multiple choice type | 11 | Sections 1.1–1.7 |
| Exercise 1(B) | 25 | Sections 1.8–1.13 |
| Multiple choice type | 17 | Sections 1.8–1.13 |
| Multiple choice type (simple pendulum) | 12 | Section 1.14 |
Exercise 1(A) covers units, prefixes and conversions. Exercise 1(B) covers least count, vernier callipers and screw gauge, including the numerical problems on zero error. The multiple choice sets test the same ranges quickly. You can work through every block in the Class 9 Physics collection, check the full Class 9 book list for the accompanying texts, or browse the Class 9 hub for all subjects. For syllabus structure and examination updates, refer to the official CISCE website.
Frequently asked questions
How do I correct a reading when a vernier callipers has negative zero error?
Subtract the zero error with its sign from the observed reading. A negative zero error such as −0.04 cm is subtracted by adding it: \text{observed} - (-0.04) = \text{observed} + 0.04\ \text{cm}. So a reading of 4.25 cm becomes 4.29 cm.
What is the difference between a light year and an astronomical unit?
Both are units of distance. An astronomical unit is the mean distance between the earth and the sun, 1.496 \times 10^{11}\ \text{m}. A light year is the distance light travels in one year, 9.46 \times 10^{15}\ \text{m} — roughly 63,000 astronomical units.
Why is a seconds’ pendulum about 1 metre long?
A seconds’ pendulum has a time period of exactly 2 s. From T = 2\pi\sqrt{l/g}, with g = 9.8\ \text{m s}^{-2}, the length comes out to about 0.994 m. That is why the text gives the length as nearly 1 metre.
Why do we measure the time for 20 oscillations of a pendulum instead of one?
A single oscillation is brief, so the stopwatch’s least count causes a large percentage error. Timing 20 oscillations and then dividing by 20 gives T = t/20, which is far more reliable.
Will the year 2100 be a leap year?
No. A year divisible by 4 is a leap year, but century years are leap years only when divisible by 400. Since 2100 fails that test, it will not have 29 days in February. The year 2000 passed the test and was a leap year.
Reference: ICSE Class 9 Physics textbook material, chapter 1: Measurements and Experimentation — CISCE-aligned.