Question

What are dimensional variables

Answer 1

In the given question we will discuss about the dimensional variables, although the Dimensional analysis is utmost often used in chemistry and physics and also in the mathematics thereof but discover some more applications outside of these fields as well.

Complete answer:
Those variables are known as Dimensional variables whose quantities have dimensions and whose numerical value might change such as Speed of a vehicle, velocity of a bus, acceleration etc., are dimensional variables.

The expression which shows the powers to the fundamental units are to be raised to obtain one unit of a derived quantity is called the dimensional formula of that quantity.
So, the $Q$is the unit of a derived quantity represented by
$Q = {M^a}{L^b}{T^c}$,
then ${M^a}{L^b}{T^c}$ is called dimensional formula and
the exponents $a,{\text{ }}b,{\text{ }}c$are called the dimensions.

Dimensional variables are the physical quantities having dimensions of the form of ${M^a}{L^b}{T^c}$where, $M,L,T$are essential physical quantities which are Mass, Length and Time correspondingly. And $a,{\text{ }}b,{\text{ }}c$are any real numbers but are variables too. We can understand it by an example as Force is a dimensional variable so it has a dimension of $1,1, - 2$for mass, length and time separately, in the essence ${M^1}{L^1}{T^{ - 2}}$. But it is a variable as the gravitational force between earth and the sun is different from the moon and the earth and another example would be mass.

Note: The Dimensional variables are those physical quantities which does have dimensions and do not have a specific fixed value such as power, acceleration, velocity, force, work, and so on. So, the physical quantities which take dimensions and have a certain amount of fixed value are to be called as dimensional constants such as Velocity of light in a vacuum$\left( C \right)$, Gravitational constant $\left( G \right)$, Universal gas constant $\left( R \right)$, Planck’s constant $\left( h \right)$and others.