Units And Dimensions: What Is It All About?
You clicking on this article means you’re probably just starting what will be the most stressful two years of your life. So, welcome to Physics! And what better way to delve into this beautiful jungle than units and dimensions!
Picturing Physics without units and dimensions is like having fries without ketchup – it’s beyond the realm of human thought and imagination. Units are what help us quantify the stuff that we need to measure and work with. By definition, any standard and universally accepted measure of a physical quantity is taken as a unit.
Fundamental units are a set of independent units that form the basis of all the other units.
|PHYSICAL QUANTITY||SYMBOL||DIMENSION||MEASUREMENT UNIT||UNIT|
Amount of Substance
Radian and steradian are two supplementary fundamental units. It measures plane angle and solid angle respectively.
|S.No.||Supplementary Fundamental Quantities||Supplementary Unit||Symbol|
Those physical quantities which are derived from fundamental quantities are called derived quantities and their units are called derived units.
e.g., velocity, acceleration, force, work etc.
For detailed definitions of each fundamental unit, please refer your prescribed textbook.
The dimensions of a unit are the combination in which the different fundamental units are multiplied to obtain said unit.
|For Work or energy, Joule [J] = [ML^2T^2]
Applications of Dimensions
- To check the accuracy of physical equations.
- To change a physical quantity from one system of units to another system of units.
- To obtain a relation between different physical quantities.
We now come to the important, albeit slightly dry part (yes, you weren’t there already).
In the measured value of a physical quantity, the number of digits about the correctness of which we are sure plus the next doubtful digit, are called the significant figures.
Rules for Finding Significant Figures
- All non-zeros digits are significant figures, e.g., 4362 m has 4 significant figures.
- All zeros occuring between non-zero digits are significant figures, e.g., 1005 has 4 significant figures.
- All zeros to the right of the last non-zero digit are not significant, e.g., 6250 has only 3 significant figures.
- In a digit less than one, all zeros to the right of the decimal point and to the left of a non-zero digit are not significant, e.g., 0.00325 has only 3 significant figures.
- All zeros to the right of a non-zero digit in the decimal part are significant, e.g., 1.4750 has 5 significant figures.
Now we come to the term you will use the most once you inevitably figure out that engineering is not right for you:
The difference between the measured and true values of any quantity is the absolute error.
Mean Absolute Error
The arithmetic mean of the magnitude of absolute errors in all the measurement is called mean absolute error.
The ratio of mean absolute error to the true value is called relative
The relative error expressed in percentage is called percentage error.
Propagation of error:
For any quantity which depends on the measurement of more than one quantity, the net error is the sum of errors of each of the components.
(i) Error in Addition or Subtraction Let x = a + b or x = a – b
If the measured values of two quantities a and b are (a ± Δa and (b ± Δb), then maximum absolute error in their addition or subtraction.
Δx = ±(Δa + Δb)
(ii) Error in Multiplication or Division Let x = a x b or x = (a/b).
If the measured values of a and b are (a ± Δa) and (b ± Δb), then maximum relative error
So there’s the gist of what you need to know in units and dimensions, in case you need to revise just before an exam or something. For more in depth details, refer to NCERT or any of your prescribed textbooks.
Go through our list of must-have books for a JEE Advanced aspirant here.