Units and Measurements
1. Physical Quantity
A quantity that can be measured and described using laws of physics.
Examples: length, mass, time, temperature, etc.
2. Units
- Fundamental Units: Cannot be derived (e.g. metre, kilogram, second).
- Derived Units: Formed by combining fundamental units (e.g. m/s, N, J).
3. SI Base Units
| Quantity | SI Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Luminous intensity | candela | cd |
| Amount of substance | mole | mol |
4. Dimensional Formula
Expression of a physical quantity in terms of base dimensions (M, L, T).
Example: Force → [M1L1T-2]
5. Significant Figures
- All non-zero digits are significant.
- Zeros between digits are significant.
- Leading zeros are not significant.
- Trailing zeros are significant if a decimal is present.
6. Common Dimensional Formulas
| Quantity | Dimensional Formula |
|---|---|
| Velocity | [M0L1T-1] |
| Acceleration | [M0L1T-2] |
| Force | [M1L1T-2] |
| Work | [M1L2T-2] |
| Power | [M1L2T-3] |
| Pressure | [M1L-1T-2] |
| Density | [M1L-3T0] |
7. Errors in Measurement
- Systematic Errors: Predictable and consistent errors.
- Random Errors: Unpredictable variations in measurements.
- Gross Errors: Due to human mistakes or instrument handling.
8. Instruments for Measurement
Vernier Caliper and Screw Gauge are used for small measurements.
Important to know their least count and how to take readings.
9. Uses of Dimensional Analysis
- To convert units.
- To check correctness of equations (dimensional consistency).
- To derive relations between physical quantities.
10. Limitations of Dimensional Analysis
- Cannot find dimensionless constants.
- Cannot determine exact formula.
- Fails when more than one quantity affects the result.