Question

How is the dimensional formula caculated?

Answer 1

The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity. The dimension of mass, length and time are represented as [M], [L] and [T] respectively. For example:

velocity = displacement /time=[L]/[T]=[L][T-1]= [mo L T1 ]


We say that dimension of velocity are, zero in mass, 1 in length and -1 in time.

Answer 2

To find the dimensional formula for any physical quantity we must know about the following things for the same..
1 - Basic knowledge of power and exponent
i.e, you must know the identities related to power and exponent

2 - Dimensions of Basic and Derived Physical quatities
for example -> Dimension of Mass is [M] which is a Basics quantity...and Dimension of Velocity is [LT^-1] which is a Derived quantity..

3- This is very important while writing Dimensions of any physical quantity you must know know its relation or formula...you cannot write Dimension unitill u know the relation or formula...

For example - Force = mass × acceleration
Dimension of mass = [M]
Dimension of acceleration = [LT^-2]

Dimesion of Force = [M] × [LT^-2]
= [MLT^-2](read as M L T minus 2 i.e, raised to the power -2l

If i ask you to write the dimesion of G which is a Universal Gravitional Constant...You cannot write the dimension of this quantity until You know in which relation this G exist..

As we know that F = G x m1 x m2 / r^2

From above relation we can find out the value of G as G = F x r^2 / m1 x m2
Now we must have knowledge of dimesion of each quantity in the above relation...
F = [MLT^-2]
r^2 = r is a distance which is actually a length so its dimension is [L]..But its r squared..so dimesion will be [L^2]
m1 and m2 are masses and dimesion of mass is [M].

Now we can write the dimension formula for the G as G = [MLT^-2] x [L^2] / [M] x [M]
=[ML^3T^-2] / [M^2]
=[M^-1 L^3 T^-2]
This is how we calculated Dimesional formula of any physical quantity...

Hope this help...