What do you understand by Dimensional Analysis? Explain with a suitable example.
- $$\text{Dimensional Analysis the study of the relationship between physical quantities with the help of dimensions and}$$ $$\text{units of measurement is termed as dimensional analysis. Dimensional analysis is essential because it keeps the}$$ $$\text{units the same, helping us perform mathematical calculations smoothly.}$$
- Unit Conversion and Dimensional Analysis
Dimensional analysis is also called Factor Label Method or Unit Factor Method because we use conversion factors to get the same units. To help you understand the stated better, let’s say you want to know how many meters make 3 km?
We know that 1000 meters make 1 km,
Therefore,
$$\text{3 km = 3 × 1000 meters = 3000 meters}$$
$$\text{Here, the conversion factor is 1000 meters.}$$
- Using Dimensional Analysis to Check the Correctness of Physical Equation
Let’s say that you don’t remember whether
$$\text{time = speed/distance, or time = distance/speed}$$
We can check this by making sure the dimensions on each side of the equations match. Reducing both the equations to its fundamental units on each side of the equation, we get
$$[T]=\dfrac{[L][T]^{-1}}{[L]}=[T]^{-1}(Wrong)$$
$$[T]=\dfrac{[L]}{[L][T]^{-1}}=[T](Right)$$
However, it should be kept in mind that dimensional analysis cannot help you determine any dimensionless constants in the equation.