9th Class Physics Chapter 1 Notes: Physical Quantities and Measurements (Punjab Board)

Chapter at a glance

The Punjab textbook for this class is the same for every board, so these notes help students of the nine boards below. Your teacher may mark a small topic as not included in your school, so follow your own textbook and date sheet for the final list.

Key concepts and definitions

• Physics is the branch of science that studies matter, energy and the way they interact. Its main branches include mechanics, heat, light, sound, electricity and magnetism, and atomic and nuclear physics.
• Physical quantity: a quantity that can be measured. A measurement has a number (magnitude) and a unit. Length, mass, time and temperature are physical quantities. Honesty or beauty cannot be measured, so they are not physical quantities.
• Base quantities are independent quantities that are taken as the starting point of measurement. Derived quantities are formed from the base quantities, for example area, volume, speed and density.
• SI (International System of Units) is the system of units agreed for use all over the world. It is based on the metre, kilogram and second along with four other base units.
• Scientific notation writes a number as a × 10ⁿ, where a is at least 1 and less than 10, and n is a whole number.
• Least count is the smallest value an instrument can measure correctly.
• Zero error: the reading an instrument shows when it should read zero. It must be removed from every observation.
• Accuracy tells how close a measurement is to the true value. Precision tells how close repeated readings are to each other.
• Error is the difference between the measured value and the true value. Faulty instruments and zero error give systematic errors; reaction time with a stopwatch gives random errors.

SI base units and prefixes

Prefixes make very large or very small values easy to write:

Note that the kilogram, not the gram, is the base unit of mass. Some derived units you will use later are the newton (N = kg m s⁻²), the pascal (Pa = N m⁻²) and the joule (J = N m).

Formulas and rules to remember

Instruments explained step by step

Where the least count of a vernier caliper comes from

1. Let one main scale division (MSD) be 1 mm.
2. Suppose 10 vernier scale divisions (VSD) fit exactly into 9 MSD, which is 9 mm.
3. Then 1 VSD = 9 ÷ 10 = 0.9 mm.
4. Least count = 1 MSD − 1 VSD = 1 − 0.9 = 0.1 mm = 0.01 cm.

The general result is LC = (smallest main scale division) ÷ (number of vernier divisions).

Taking a vernier reading

1. Close the jaws and note the zero error first.
2. Place the object between the jaws and read the main scale just before the vernier zero (MSR).
3. Find the vernier line that exactly meets a main scale line. Call its number n.
4. Reading = MSR + n × LC. Then subtract the zero error.

With 10 vernier divisions, a vernier zero to the right of the main zero gives a positive zero error of +n × LC, where n is the coinciding line. If the vernier zero is to the left and the m-th line coincides, the zero error is −(10 − m) × LC. The corrected reading is always observed reading minus zero error, so a negative error is added.

Screw gauge

The pitch is the distance the spindle moves forward in one full turn. A common screw gauge has a pitch of 1 mm and 100 circular divisions, so LC = 1 ÷ 100 = 0.01 mm. If the circular scale reads n divisions when the gap is closed and n is small, the error is +n × LC. If it reads close to 100, for example 97, the error is −(100 − 97) × LC = −0.03 mm.

Other instruments

• Meter rule: least count 1 mm. Keep your eye straight above the mark to avoid parallax error.
• Physical balance: compares the unknown mass with standard masses.
• Stopwatch: measures a time interval. A digital one often reads to 0.01 s, but your reaction time is usually larger than that.
• Measuring cylinder: read the liquid level at eye level, at the lowest point of the curved surface for water. The volume of an irregular solid that sinks is V₂ − V₁.

Significant figures

• All non-zero digits are significant.
• Zeros between non-zero digits are significant (3004 has four).
• Leading zeros are not significant (0.0042 has two).
• Trailing zeros after a decimal point are significant (25.00 has four).
• In multiplication and division, keep as many significant figures as the least precise value has.
• In addition and subtraction, keep as many decimal places as the value with the fewest decimal places.

Solved numericals

Numerical 1: vernier caliper

A vernier caliper has LC = 0.01 cm. For a cylinder, the main scale reads 2.4 cm and the 6th vernier line coincides. With the jaws closed, the 2nd vernier line coincides. Find the corrected diameter.

Zero error = +2 × 0.01 = +0.02 cm. Observed reading = 2.4 + 6 × 0.01 = 2.46 cm. Corrected reading = 2.46 − 0.02 = 2.44 cm.

Numerical 2: screw gauge

A screw gauge has pitch 1 mm and 100 circular divisions. For a wire, the linear scale shows 3 mm and the circular scale shows 27 divisions. With the gap closed the circular scale reads 97. Find the diameter.

LC = 1 ÷ 100 = 0.01 mm. Zero error = −(100 − 97) × 0.01 = −0.03 mm. Observed reading = 3 + 27 × 0.01 = 3.27 mm. Corrected reading = 3.27 − (−0.03) = 3.30 mm.

Numerical 3: scientific notation and conversions

1. 0.00056 g in kg: 0.00056 g = 5.6 × 10⁻⁴ g. Since 1 g = 10⁻³ kg, the mass is 5.6 × 10⁻⁴ × 10⁻³ = 5.6 × 10⁻⁷ kg.
2. 72 km/h in m/s: 72 × 1000 ÷ 3600 = 20 m/s.
3. 3 × 10⁸ m/s in km/h: 3 × 10⁸ × 3600 ÷ 1000 = 3 × 10⁸ × 3.6 = 10.8 × 10⁸ = 1.08 × 10⁹ km/h.

Numerical 4: significant figures

Counts: 0.00450 has 3; 3004 has 4; 25.00 has 4; 6.02 × 10²³ has 3. A rectangle measures 4.5 m by 2.34 m. Area = 4.5 × 2.34 = 10.53 m². The value 4.5 has 2 significant figures, so the answer is 11 m². For addition, 12.52 + 1.7 = 14.22, and the least number of decimal places is one, so the answer is 14.2.

Numerical 5: density with unit conversion

A block of 10 cm × 5.0 cm × 4.0 cm has a mass of 540 g. Find its density in kg m⁻³.

Volume = 10 × 5.0 × 4.0 = 200 cm³. Density = 540 ÷ 200 = 2.7 g cm⁻³. Because 1 g cm⁻³ = 10⁻³ kg ÷ 10⁻⁶ m³ = 10³ kg m⁻³, the density is 2700 kg m⁻³.

Common mistakes

• Writing the SI unit of mass as the gram. It is the kilogram.
• Forgetting the sign of the zero error, or subtracting a negative error instead of adding it.
• Choosing the vernier line that is nearest the zero instead of the one that meets a main scale line exactly.
• Counting leading zeros as significant figures.
• Writing 12 × 10³ as scientific notation. The first number must be between 1 and 10.
• Mixing µ (micro, 10⁻⁶) with m (milli, 10⁻³).
• Using cm in one place and m in another in the same formula.
• Reading a measuring cylinder from above or below eye level.

Questions to practise

Short questions

1. Define a physical quantity and give two examples.
2. Differentiate between base and derived quantities.
3. Write the seven SI base quantities with their units and symbols.
4. Why are prefixes used? Write the value of kilo, milli, micro and nano.
5. Express 0.00025 s and 4 500 000 m in scientific notation.
6. What is the least count of an instrument? How is it found for a vernier caliper?
7. What is zero error? How is a reading corrected for it?
8. Define the pitch of a screw gauge.
9. State the rules for zeros in significant figures.
10. Differentiate between accuracy and precision.
11. How can you find the volume of a small irregular stone with a measuring cylinder?

Long questions

1. Describe a vernier caliper. Explain how to find its least count, take a reading and correct the zero error.
2. Describe a screw gauge and explain how to measure the diameter of a wire with it.
3. Explain the SI system with examples of base and derived units. Write the units of density and pressure in base units.
4. Explain significant figures and the rules for using them in calculations, with examples.

Numericals to try

1. Convert 2.5 km into metres and into millimetres. Write both in scientific notation.
2. A vernier caliper has 20 vernier divisions equal to 19 main scale divisions of 1 mm each. Find its least count.
3. A screw gauge has a pitch of 0.5 mm and 50 circular divisions. Find its least count and the reading for 4 linear divisions and 18 circular divisions.
4. Find the number of significant figures in 0.0070, 1.050 and 800.
5. A solid of mass 0.27 kg occupies 100 cm³. Find its density in kg m⁻³.

Practice MCQs

Try these first. The answer key is at the end of the article.

1. Which of the following is a base quantity?
   A) Force
   B) Speed
   C) Time
   D) Area
2. The SI unit of electric current is
   A) volt
   B) ampere
   C) ohm
   D) coulomb
3. 5.6 × 10⁻³ m is equal to
   A) 0.56 mm
   B) 5.6 mm
   C) 56 mm
   D) 560 mm
4. One main scale division is 1 mm and 10 vernier divisions equal 9 main scale divisions. The least count is
   A) 1 mm
   B) 0.5 mm
   C) 0.1 mm
   D) 0.01 mm
5. The number of significant figures in 0.0305 is
   A) 2
   B) 3
   C) 4
   D) 5
6. The SI unit of density in base units is
   A) kg m⁻²
   B) kg m⁻³
   C) g cm⁻³
   D) kg m³
7. The prefix nano stands for
   A) 10⁻³
   B) 10⁻⁶
   C) 10⁻⁹
   D) 10⁻¹²
8. A screw gauge has a pitch of 1 mm and 50 divisions on the circular scale. Its least count is
   A) 0.5 mm
   B) 0.2 mm
   C) 0.02 mm
   D) 0.002 mm

Preparation strategy

1. Day 1: learn the seven base units, symbols and prefixes. Write them from memory.
2. Day 2: practise the vernier caliper with the least count derivation and three readings, including a zero error.
3. Day 3: do the same for the screw gauge.
4. Day 4: do scientific notation, conversions and significant figures.
5. Day 5: attempt the chapter MCQs and short questions, then redo the ones you missed.

For the complete picture of the class, read the 9th class Physics textbook guideand the 9th class Physics pairing scheme.

Diagram ideas

• Labelled vernier caliper. Alt text: "Vernier caliper with the jaws, main scale, vernier scale, depth rod and locking screw labelled."
• Vernier reading example. Alt text: "Close-up of a vernier scale with the sixth line meeting a main scale line, showing how the reading is added."
• Zero error cases. Alt text: "Three closed vernier calipers showing no error, positive zero error and negative zero error."
• Labelled screw gauge. Alt text: "Screw gauge with the frame, anvil, spindle, linear scale, circular scale and ratchet labelled."
• Measuring cylinder. Alt text: "Measuring cylinder with water, an eye at the level of the lower meniscus and a stone being lowered in."
• SI table. Alt text: "Chart of the seven SI base quantities with their units and symbols."

MCQ answer key

1. C. Length, mass and time are base quantities. Force, speed and area are derived.
2. B. The ampere (A) is the base unit of electric current.
3. B. 10⁻³ m is 1 mm, so 5.6 × 10⁻³ m is 5.6 mm.
4. C. 1 VSD = 0.9 mm, so least count = 1 − 0.9 = 0.1 mm.
5. B. Leading zeros do not count. The digits 3, 0 and 5 give three significant figures.
6. B. Density is mass divided by volume, so kg / m³ = kg m⁻³.
7. C. Nano means one billionth, 10⁻⁹.
8. C. Least count = pitch / divisions = 1 mm / 50 = 0.02 mm.

Frequently asked questions