Units And Dimensions 1 Notes
| Exam: JENPAS | Subject: Physics | Topic: Units And Dimensions 1 | Type: Short Notes |
Units, Measurements, Errors and Dimensions
This short note is made for JENPAS UG Nursing exam preparation from Class 11 Physics. It covers the most important concepts, definitions, and formulas from the chapter in a quick revision format.
Physical quantity is any quantity that can be measured.
Unit is the standard reference used to measure a physical quantity.
Examples of physical quantities: length, mass, time, force, energy, velocity.
Exam Tip: Learn definitions clearly.Fundamental quantities are independent quantities that do not depend on any other quantity.
Examples: length, mass, time, electric current, temperature, amount of substance, luminous intensity.
Derived quantities are formed from fundamental quantities.
Examples: velocity, acceleration, force, work, pressure.
CGS system = centimetre, gram, second.
MKS system = metre, kilogram, second.
SI system = International System of Units and is the most widely used system. SI uses seven base units including metre, kilogram, second, ampere, kelvin, mole, and candela.
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| 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 |
Significant figures are the meaningful digits in a measured quantity.
- All non-zero digits are significant.
- Zeros between two non-zero digits are significant.
- Zeros on the left side are not significant.
- Trailing zeros in a decimal number are significant.
Example: 0.00450 has 3 significant figures.
Error is the difference between the true value and the measured value of a physical quantity.
Absolute error is the magnitude of this difference.
Mean absolute error is the arithmetic mean of all absolute errors.
Relative error is the ratio of mean absolute error to the mean value.
Percentage error = relative error × 100.
$$ a_{mean} = \frac{a_1 + a_2 + a_3 + \cdots + a_n}{n} $$
$$ \Delta a_i = |a_i - a_{mean}| $$
$$ \Delta a_{mean} = \frac{|\Delta a_1| + |\Delta a_2| + \cdots + |\Delta a_n|}{n} $$
$$ \text{Relative error} = \frac{\Delta a_{mean}}{a_{mean}} $$
$$ \text{Percentage error} = \frac{\Delta a_{mean}}{a_{mean}} \times 100 $$
For sum or difference:
$$ Z = A \pm B $$
$$ \Delta Z = \Delta A + \Delta B $$
For product:
$$ Z = AB $$
$$ \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B} $$
For division:
$$ Z = \frac{A}{B} $$
$$ \frac{\Delta Z}{Z} = \frac{\Delta A}{A} + \frac{\Delta B}{B} $$
For powers:
$$ Z = \frac{A^p B^q}{C^r} $$
$$ \frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B} + r\frac{\Delta C}{C} $$
Dimension of a physical quantity shows how it depends on fundamental quantities like mass, length, and time.
It is written in the form [MaLbTc].
Principle of dimensional homogeneity: both sides of a physical equation must have the same dimensions.
| Quantity | Dimensional Formula |
|---|---|
| Velocity | [LT-1] |
| Acceleration | [LT-2] |
| Force | [MLT-2] |
| Momentum | [MLT-1] |
| Work / Energy | [ML2T-2] |
| Power | [ML2T-3] |
| Pressure | [ML-1T-2] |
| Angular velocity | [T-1] |
- To check whether a physical equation is dimensionally correct.
- To derive relations between physical quantities.
- To convert one system of units into another.
- To find the dimension of unknown quantities.
Plane angle:
$$ d\theta = \frac{ds}{r} $$
Solid angle:
$$ d\Omega = \frac{dA}{r^2} $$
Parallax method:
$$ D = \frac{d}{\theta} $$
- Unit is the standard of measurement.
- SI is the standard international system.
- Absolute error measures actual difference.
- Relative error is a ratio.
- Percentage error = relative error × 100.
- Dimensional analysis checks correctness of formula.
- Both sides of an equation must have the same dimensions.