Units and Measurement

Overview

Units and Measurement forms the foundational chapter of physics and is essential for MAHA TET Paper II (Mathematics and Science). This topic tests your understanding of how physical quantities are expressed, the International System of Units (SI), and practical measurement techniques for length, mass, time, and temperature.

For the exam, expect direct questions on SI base units, their symbols, conversion between units, and the correct use of measuring instruments. Questions often appear as fill-in-the-blanks, match-the-columns, or simple numerical conversions. Mastery here also supports later topics like motion, force, and heat, where correct unit handling is critical.

Students must be able to distinguish between fundamental and derived quantities, recall SI units with correct symbols, perform unit conversions confidently, and understand the principles behind common measuring instruments used in school laboratories.

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Key Concepts

• **Physical Quantity**: Any quantity that can be measured and expressed in numbers with a unit (e.g., length = 5 metres).

• **Fundamental (Base) Quantities**: Quantities that are independent and cannot be derived from other quantities. SI has seven base quantities: length, mass, time, electric current, temperature, amount of substance, and luminous intensity.

• **Derived Quantities**: Quantities obtained by combining fundamental quantities through multiplication or division (e.g., speed = length ÷ time, area = length × length).

• **SI System (Système International)**: The internationally accepted system of units adopted in 1960. India officially uses SI units.

• **Standard Unit**: A fixed and universally accepted reference for measurement. For example, the metre is defined based on the speed of light.

• **Precision vs Accuracy**: Precision refers to how close repeated measurements are to each other; accuracy refers to how close a measurement is to the true value.

• **Least Count**: The smallest measurement that an instrument can make. For a standard ruler, least count = 1 mm = 0.1 cm.

• **Significant Figures**: The meaningful digits in a measured value that indicate the precision of measurement.

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Formulas / Key Facts

### SI Base Units for MAHA TET

| Physical Quantity | SI Unit | Symbol | |-------------------|---------|--------| | Length | metre | m | | Mass | kilogram | kg | | Time | second | s | | Temperature | kelvin | K | | Electric Current | ampere | A | | Amount of Substance | mole | mol | | Luminous Intensity | candela | cd |

### Common Derived Units

| Quantity | Formula | SI Unit | |----------|---------|---------| | Area | length × length | m² | | Volume | length × length × length | m³ | | Speed | distance ÷ time | m/s | | Density | mass ÷ volume | kg/m³ |

### Length Conversions

• 1 kilometre (km) = 1000 metres (m)
• 1 metre (m) = 100 centimetres (cm)
• 1 centimetre (cm) = 10 millimetres (mm)
• 1 metre = 1000 millimetres

### Mass Conversions

• 1 kilogram (kg) = 1000 grams (g)
• 1 gram (g) = 1000 milligrams (mg)
• 1 quintal = 100 kg
• 1 metric tonne = 1000 kg

### Time Conversions

• 1 hour = 60 minutes = 3600 seconds
• 1 minute = 60 seconds
• 1 day = 24 hours = 86400 seconds

### Temperature Conversions

• Celsius to Kelvin: K = °C + 273
• Kelvin to Celsius: °C = K − 273
• Celsius to Fahrenheit: °F = (9/5 × °C) + 32
• Fahrenheit to Celsius: °C = 5/9 × (°F − 32)

### Measuring Instruments

• **Length**: Metre scale, measuring tape, vernier calliper, screw gauge
• **Mass**: Beam balance, electronic balance, spring balance (measures weight)
• **Time**: Stopwatch, pendulum clock, digital clock
• **Temperature**: Mercury thermometer, digital thermometer (clinical thermometer range: 35°C to 42°C)

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Worked Examples

**Example 1: Unit Conversion (Length)** Convert 2.5 kilometres into metres.

Solution: 1 km = 1000 m 2.5 km = 2.5 × 1000 = **2500 m**

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**Example 2: Temperature Conversion** Convert 37°C (normal body temperature) to Kelvin and Fahrenheit.

Solution: Kelvin = °C + 273 = 37 + 273 = **310 K** Fahrenheit = (9/5 × 37) + 32 = 66.6 + 32 = **98.6°F**

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**Example 3: Identifying Correct Units** A student measures the volume of a box as 500. What is the correct SI unit?

Solution: Volume = length × length × length SI unit of length = metre SI unit of volume = metre × metre × metre = **m³** (cubic metre)

If measured in cm, write as cm³. But SI unit is always m³.

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Common Mistakes

• **Confusing kg with g as the base unit** → The SI base unit of mass is kilogram (kg), not gram. Gram is a sub-unit.

• **Writing unit symbols incorrectly** → Symbols are case-sensitive: "m" for metre (not "M"), "K" for kelvin (not "k"), "s" for second (not "S" or "sec").

• **Adding 273.15 instead of 273 in school-level problems** → For MAHA TET, use K = °C + 273 (simplified). Only advanced physics uses 273.15.

• **Forgetting that temperature has no degree symbol in Kelvin** → Write "310 K" not "310°K". The degree symbol is used only with Celsius and Fahrenheit.

• **Confusing weight and mass** → Mass is measured in kg and is constant everywhere. Weight is a force measured in newtons (N) and changes with gravity. Spring balance measures weight, not mass.

• **Mixing up metre scale least count** → Standard metre scale has least count of 1 mm (0.1 cm), not 1 cm.

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Quick Reference

1. **Seven SI base units**: metre, kilogram, second, kelvin, ampere, mole, candela.

2. **SI unit of length is metre (m)**, mass is kilogram (kg), time is second (s), temperature is kelvin (K).

3. **K = °C + 273** — no degree symbol with kelvin.

4. **1 km = 1000 m; 1 kg = 1000 g; 1 hour = 3600 s**.

5. **Least count of metre scale = 1 mm = 0.1 cm**.

6. **Derived units come from base units**: area (m²), volume (m³), speed (m/s), density (kg/m³).