Physical Quantities and Measurement
1. What is Measurement?
Measurement is the process of comparing an unknown quantity with a known standard (unit).
A physical quantity is a quantity that can be measured. Examples: length, mass, time, temperature, area, volume.
To measure a quantity, we need:
- A unit (standard of comparison).
- A device (instrument to measure).
2. The International System of Units (SI)
The SI system is the globally accepted system of measurement.
Base SI Units
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Temperature | kelvin | K |
| Electric current | ampere | A |
Common Prefixes
| Prefix | Symbol | Factor |
|---|---|---|
| kilo | k | 1000 |
| centi | c | 1/100 |
| milli | m | 1/1000 |
| micro | mu | 1/1,000,000 |
Example: 1 km = 1000 m, 1 cm = 1/100 m = 0.01 m, 1 mm = 1/1000 m = 0.001 m.
Common Mistake: Writing 'kg' as 'KG' or 'Kg'. The correct symbol for kilogram is 'kg' (lowercase k).
3. Measuring Length
Instruments for Measuring Length
| Instrument | Used For | Least Count |
|---|---|---|
| Metre scale/ruler | Everyday lengths | 1 mm (0.1 cm) |
| Measuring tape | Longer lengths (tailor, survey) | 1 mm (0.1 cm) |
| Vernier callipers | Precise measurements (up to 0.1 mm) | 0.1 mm |
| Micrometer screw gauge | Very precise measurements (up to 0.01 mm) | 0.01 mm |
Correct Way to Use a Ruler
- Place the ruler flat against the object.
- Keep your eye directly above the marking to avoid parallax error.
- Measure from the 0 mark (not the edge of the ruler).
Worked Example: A pencil measures from 2 cm to 14.5 cm on a ruler. What is its length?
Length = 14.5 - 2.0 = 12.5 cm.
4. Measuring Mass
Mass is the amount of matter in a body. It is measured using a balance.
| Instrument | Use |
|---|---|
| Beam balance | Comparing masses |
| Spring balance | Measuring weight (force) |
| Electronic balance | Digital, precise mass measurement |
| Kitchen scale | Everyday weighing |
Units of mass: 1 kg = 1000 g, 1 g = 1000 mg, 1 quintal = 100 kg, 1 tonne = 1000 kg.
Difference: Mass vs Weight
| Mass | Weight |
|---|---|
| Amount of matter | Force of gravity on the mass |
| Constant everywhere | Changes with location |
| Measured in kg | Measured in newton (N) |
5. Measuring Time
Time is measured using clocks. SI unit: second (s).
| Instrument | Measures |
|---|---|
| Pendulum clock | Time intervals |
| Stopwatch | Short time intervals (races, experiments) |
| Digital watch | Precise time |
Pendulum: A simple pendulum has a bob suspended by a string.
Time period (T) = time taken for one complete oscillation.
Worked Example: A pendulum completes 20 oscillations in 40 seconds. Find its time period.
T = Total time / Number of oscillations = 40 / 20 = 2 seconds.
6. Measuring Temperature
Temperature is the degree of hotness or coldness of a body.
Thermometer is used to measure temperature.
| Scale | Freezing point of water | Boiling point of water |
|---|---|---|
| Celsius (C) | 0 | 100 |
| Fahrenheit (F) | 32 | 212 |
| Kelvin (K) | 273 | 373 |
Exam Focus (2 marks): 'Convert 37 C to Kelvin.'
K = C + 273 = 37 + 273 = 310 K.
7. Volume Measurement
Volume is the amount of space occupied by a substance.
Unit: cubic metre (m^3).
1 litre (L) = 1000 mL = 1000 cm^3.
1 m^3 = 1000 L.
Measuring volume of liquids: Measuring cylinder, beaker.
Measuring volume of irregular solids: Displacement method.
Worked Example: A stone is placed in a measuring cylinder with 50 mL water. The water level rises to 68 mL. Find the volume of the stone.
Volume of stone = 68 - 50 = 18 mL = 18 cm^3.
Common Mistake: Reading the meniscus incorrectly. For water, read the bottom of the meniscus (curved surface) at eye level.
8. Self-Test
- What is the SI unit of: (a) length (b) mass (c) time?
- Convert: (a) 3.5 km to m (b) 450 cm to m (c) 2500 g to kg.
- A pendulum takes 30 seconds for 15 oscillations. Find its time period.
- Convert 98.6 F to Celsius. (Formula: C = (F - 32) x 5/9)
- Differentiate between mass and weight.
- An irregular stone displaces water from 30 mL to 52 mL in a measuring cylinder. Find its volume.
- What is parallax error? How can it be avoided?
9. Answers to Self-Test
- (a) metre (m) (b) kilogram (kg) (c) second (s).
- (a) 3500 m (b) 4.5 m (c) 2.5 kg.
- T = 30 / 15 = 2 seconds.
- C = (98.6 - 32) x 5/9 = 66.6 x 5/9 = 37 C.
- Mass is amount of matter (constant), weight is gravitational force (varies). Mass in kg, weight in N.
- Volume = 52 - 30 = 22 mL = 22 cm^3.
- Parallax error occurs when the eye is not directly above the measurement mark. Avoid by keeping the eye level with the marking.
