Physical Quantities and Measurement
1. Physical Quantities
A PHYSICAL QUANTITY is a quantity that can be MEASURED.
Fundamental and Derived Quantities
| Type | Definition | Examples |
|---|---|---|
| Fundamental | Cannot be expressed in terms of others | Length, Mass, Time |
| Derived | Expressed using fundamental quantities | Speed, Area, Volume, Density |
The SI System (International System of Units)
| Fundamental Quantity | SI Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Electric current | ampere | A |
2. Measurement of Length
SI Unit: metre (m)
Sub-units of Length
| Unit | Relation to Metre |
|---|---|
| 1 kilometre (km) | 1000 m |
| 1 hectometre (hm) | 100 m |
| 1 decametre (dam) | 10 m |
| 1 metre (m) | 1 m |
| 1 decimetre (dm) | 0.1 m |
| 1 centimetre (cm) | 0.01 m |
| 1 millimetre (mm) | 0.001 m |
| 1 micrometre (μm) | 10⁻⁶ m |
Instruments for Length Measurement
| Instrument | Measures | Accuracy |
|---|---|---|
| Metre scale / ruler | Length up to 1 m | 1 mm (0.1 cm) |
| Measuring tape | Length up to several metres | 1 mm |
| Vernier callipers | Small lengths (up to 15 cm) | 0.1 mm |
| Micrometer screw gauge | Very small thicknesses | 0.01 mm |
3. Measurement of Area
Area = length × breadth. SI unit: m².
Area of Regular Shapes
- Rectangle: A = l × b
- Square: A = s²
- Triangle: A = ½ × b × h
- Circle: A = πr²
Area of Irregular Shapes
Using GRAPH PAPER:
- Place the shape on graph paper.
- Count the number of FULL squares inside.
- Count half or more squares as 1, less than half as 0.
- Area = Total count × area of one square.
4. Measurement of Volume
Volume = length × breadth × height. SI unit: m³.
Units of Volume
| Unit | Equivalent |
|---|---|
| 1 m³ | 1000 litres |
| 1 litre (L) | 1000 mL, 0.001 m³ |
| 1 mL | 1 cm³ |
Measuring Volume of Liquids
- Using a measuring cylinder (graduated cylinder).
- Read the bottom of the MENISCUS (curved surface of liquid).
- For water: the meniscus is concave. Read the LOWEST point.
Measuring Volume of Irregular Solids (Displacement Method)
- Fill a measuring cylinder with water to a known volume.
- Submerge the object completely.
- The RISE in water level = volume of the object.
Density
Density = Mass / Volume. SI unit: kg/m³. 1 g/cm³ = 1000 kg/m³.
5. Measurement of Mass
Mass is the AMOUNT of matter in an object. SI unit: kg.
Comparing Mass and Weight
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of matter | Force of gravity |
| SI unit | kilogram (kg) | newton (N) |
| Changes with location | NO | YES |
| Measured using | Beam balance | Spring balance |
6. Measurement of Time
SI unit: second (s).
Time Measuring Devices
| Device | Accuracy |
|---|---|
| Pendulum clock | Moderate |
| Stopwatch | 0.1 s or 0.01 s |
| Quartz clock | Very high |
| Atomic clock | Highest (10⁻¹⁵ s) |
Simple Pendulum
A simple pendulum consists of a BOB suspended by a light, inextensible string.
Time period (T) = Time taken for ONE complete oscillation. T = 2π√(l/g), where l = length of string, g = acceleration due to gravity.
7. ICSE Exam Focus
| Topic | Marks | Frequency |
|---|---|---|
| SI units and conversions | 2 marks | Very High |
| Volume measurement (displacement) | 2-3 marks | High |
| Area of irregular shapes | 2 marks | Medium |
| Density calculations | 2-3 marks | High |
| Simple pendulum | 2 marks | Medium |
Common Mistakes
- Confusing mass and weight (mass is constant, weight changes with gravity).
- Forgetting to read the LOWER meniscus for water.
- Not converting all units to the same system before calculating density.
Self-Test (5 Questions)
Q1. The SI unit of volume is: (1 mark)
- A) litre
- B) cm³
- C) m³
- D) mL
Q2. Convert 5000 cm³ to litres. (1 mark)
Q3. 'A stone is submerged in water. Initial level = 50 mL, final = 78 mL. Volume of stone?' (2 marks)
Q4. 'Find density of an object with mass 200 g and volume 50 cm³.' (2 marks)
Q5. 'A simple pendulum takes 40 s for 20 oscillations. Find its time period.' (2 marks)
Answers
A1. C) m³. A2. 5 litres. (1000 cm³ = 1 L. 5000 cm³ = 5 L.) A3. 28 cm³ or 28 mL. (Volume = 78 - 50 = 28 mL = 28 cm³.) A4. 4 g/cm³. (Density = 200/50 = 4 g/cm³.) A5. 2 s. (Time period = 40/20 = 2 s.)
