9th Class Physics Chapter 1 Physical Quantities and Measurement – Notes and MCQs (KPK New Syllabus)

Chapter 1 of 9th class Physics (KPK new syllabus) explains what physical quantities are, how they are measured in SI units, and how to report a measurement correctly using significant figures and scientific notation. Numericals on vernier calipers, screw gauge and significant figures come up almost every year in the KP board exams, so learn this chapter well.

Key Notes

1. Physical and Non-Physical Quantities

Physical quantity: A quantity that can be measured and expressed as a number with a unit, e.g. length, mass, time, temperature, force.

Non-physical quantity: A quantity that cannot be measured with an instrument, e.g. love, beauty, intelligence, fear.

Every physical quantity has two parts: a numerical value (magnitude) and a unit. Example: 5 kg (5 = magnitude, kg = unit).

2. Base and Derived Quantities

Base quantities: Quantities that are not defined in terms of other quantities. The SI system has 7 base quantities:

• Length – metre (m)
• Mass – kilogram (kg)
• Time – second (s)
• Electric current – ampere (A)
• Temperature – kelvin (K)
• Amount of substance – mole (mol)
• Luminous intensity – candela (cd)

Derived quantities: Quantities defined using base quantities, e.g. area (m²), volume (m³), speed (m/s), density (kg/m³), force (newton, N = kg m/s²).

3. International System of Units (SI)

SI is the internationally agreed system of units used by scientists all over the world. It makes measurements easy to compare and communicate.

4. Prefixes

Prefixes are words or letters placed before a unit to show multiples or sub-multiples of ten.

• giga (G) = 10^9, mega (M) = 10^6, kilo (k) = 10^3
• centi (c) = 10^-2, milli (m) = 10^-3, micro (µ) = 10^-6, nano (n) = 10^-9, pico (p) = 10^-12

Example: 5 km = 5 × 10^3 m = 5000 m; 3 ms = 3 × 10^-3 s.

5. Scientific Notation

Scientific notation is a way of writing a number as a number between 1 and 10 multiplied by a power of ten.

Examples: 45000 = 4.5 × 10^4 ; 0.00062 = 6.2 × 10^-4

6. Measuring Instruments

Least count: The smallest value an instrument can measure accurately.

• Metre rule: least count = 1 mm (0.1 cm). Keep the eye exactly above the reading to avoid parallax error.
• Vernier calipers: least count = 0.1 mm = 0.01 cm. Used for length, internal and external diameter and depth of small objects.
  Formula: Least count = smallest main scale reading ÷ number of vernier divisions = 1 mm ÷ 10 = 0.1 mm.
  Reading = main scale reading + (coinciding vernier division × least count) − zero error.
• Micrometer screw gauge: least count = 0.01 mm = 0.001 cm. Used for very small lengths such as the diameter of a thin wire.
  Formula: Least count = pitch ÷ number of circular scale divisions = 0.5 mm ÷ 50 = 0.01 mm.
• Measuring cylinder: measures volume of liquids; read at the bottom of the meniscus (for water).
• Stopwatch: measures time intervals; digital stopwatch least count is often 0.01 s.
• Physical balance / electronic balance: measures mass.

Worked Example 1 (Vernier calipers): Main scale reading = 2.3 cm, 6th vernier division coincides, least count = 0.01 cm, no zero error.
Reading = 2.3 + (6 × 0.01) = 2.3 + 0.06 = 2.36 cm.

Worked Example 2 (Screw gauge): Main scale reading = 3.5 mm, circular scale division on the line = 22, least count = 0.01 mm, zero error = +0.02 mm.
Observed reading = 3.5 + (22 × 0.01) = 3.72 mm
Corrected reading = 3.72 − 0.02 = 3.70 mm.

7. Errors and Uncertainty

Error: The difference between the measured value and the true value.

• Systematic error: Error due to a fault in the instrument or method, e.g. zero error. It shifts all readings in the same direction and cannot be removed by averaging.
• Random error: Error due to unpredictable changes (e.g. reaction time, small changes in conditions). It is reduced by taking many readings and finding their average.
• Uncertainty: The range within which the true value is expected to lie, e.g. 12.5 ± 0.1 cm.

Accuracy: How close a measurement is to the true value. Precision: How close repeated measurements are to each other (also depends on the least count of the instrument).

8. Significant Figures

Significant figures are all the accurately known digits in a measurement plus the first doubtful digit.

• All non-zero digits are significant: 248 has 3.
• Zeros between non-zero digits are significant: 2005 has 4.
• Leading zeros are not significant: 0.0045 has 2.
• Trailing zeros after a decimal point are significant: 4.500 has 4; 0.00450 has 3.

Rounding off: If the digit to be dropped is less than 5, the last kept digit stays the same (4.63 → 4.6); if it is more than 5, the last kept digit increases by one (4.67 → 4.7).

اردو میں خلاصہ

اس باب میں ہم نے پڑھا کہ طبعی مقداریں وہ ہیں جن کو ناپا جا سکے، جیسے لمبائی، کمیت اور وقت۔ ایس آئی نظام میں سات بنیادی مقداریں ہیں اور باقی تمام مقداریں انہی سے اخذ کی جاتی ہیں۔ بہت بڑی یا بہت چھوٹی مقدار لکھنے کے لیے سائنسی طریقہ تحریر اور سابقے (جیسے کلو، ملی، مائیکرو) استعمال ہوتے ہیں۔ ورنیئر کیلیپرز کا لیسٹ کاؤنٹ 0.01 سینٹی میٹر اور سکرو گیج کا 0.001 سینٹی میٹر ہوتا ہے۔ پیمائش میں غلطیاں دو قسم کی ہوتی ہیں: نظامی غلطی اور اتفاقی غلطی۔ اتفاقی غلطی کو کئی ریڈنگز کی اوسط لے کر کم کیا جا سکتا ہے۔

Important Short Questions

1. Differentiate between base and derived quantities.
   Base quantities are independent and not defined by other quantities (e.g. length, mass, time). Derived quantities are defined in terms of base quantities (e.g. speed = distance/time).
2. What is least count? Write the least count of vernier calipers and screw gauge.
   The smallest measurement an instrument can take. Vernier calipers: 0.01 cm; screw gauge: 0.001 cm.
3. What is zero error? How is it corrected?
   When the jaws (or faces) of the instrument are closed but the zero of the scales do not coincide, the instrument has zero error. It is corrected by subtracting the zero error (with its sign) from the observed reading.
4. Why is a screw gauge more precise than vernier calipers?
   Because its least count (0.001 cm) is smaller than that of vernier calipers (0.01 cm).
5. Write 0.000356 in scientific notation and state its significant figures.
   3.56 × 10^-4; it has 3 significant figures.
6. Differentiate between random and systematic error.
   Random errors occur unpredictably and are reduced by averaging; systematic errors occur due to faulty instruments or methods and affect all readings in the same way.
7. What is the difference between accuracy and precision?
   Accuracy is closeness to the true value; precision is closeness of repeated readings to one another.

20 MCQs

1. The SI unit of length is:
   (a) centimetre (b) metre (c) kilometre (d) inch
2. The number of base quantities in the SI system is:
   (a) 5 (b) 6 (c) 7 (d) 9
3. Which of the following is a derived quantity?
   (a) mass (b) time (c) velocity (d) temperature
4. 1 mm is equal to:
   (a) 10^-1 m (b) 10^-2 m (c) 10^-3 m (d) 10^-6 m
5. The prefix "mega" stands for:
   (a) 10^3 (b) 10^6 (c) 10^9 (d) 10^-6
6. The least count of vernier calipers is:
   (a) 0.1 cm (b) 0.01 cm (c) 0.001 cm (d) 1 cm
7. The least count of a micrometer screw gauge is:
   (a) 0.01 mm (b) 0.1 mm (c) 1 mm (d) 0.001 mm
8. The SI unit of temperature is:
   (a) degree Celsius (b) degree Fahrenheit (c) kelvin (d) joule
9. The SI unit of amount of substance is:
   (a) kilogram (b) mole (c) gram (d) candela
10. The number of significant figures in 0.00450 is:
    (a) 2 (b) 3 (c) 5 (d) 6
11. 45000 in scientific notation is:
    (a) 45 × 10^3 (b) 4.5 × 10^3 (c) 4.5 × 10^4 (d) 0.45 × 10^5
12. The most suitable instrument to measure the diameter of a thin wire is:
    (a) metre rule (b) measuring tape (c) vernier calipers (d) screw gauge
13. Zero error of an instrument is an example of:
    (a) random error (b) systematic error (c) human error only (d) no error
14. The volume of a liquid is measured with a:
    (a) measuring cylinder (b) screw gauge (c) stopwatch (d) balance
15. Which of the following is a non-physical quantity?
    (a) length (b) force (c) beauty (d) time
16. The SI unit of luminous intensity is:
    (a) ampere (b) candela (c) kelvin (d) mole
17. 1 nanometre is equal to:
    (a) 10^-6 m (b) 10^-9 m (c) 10^-12 m (d) 10^-3 m
18. Random errors can be reduced by:
    (a) using a faulty instrument (b) taking one reading only (c) taking the average of many readings (d) ignoring zero error
19. The least count of a metre rule is:
    (a) 1 cm (b) 1 mm (c) 0.1 mm (d) 0.01 mm
20. Which of these is a base quantity?
    (a) area (b) electric current (c) density (d) force

Answer Key

1. (b)
2. (c)
3. (c)
4. (c)
5. (b)
6. (b)
7. (a)
8. (c)
9. (b)
10. (b)
11. (c)
12. (d)
13. (b)
14. (a)
15. (c)
16. (b)
17. (b)
18. (c)
19. (b)
20. (b)

These notes are prepared by Zama Taleem as per the KP Textbook Board syllabus. Always study from your official textbook too.