How can we find the dimensions of any physical quantity in the simplest way????? Please tell me as soon as possible.

Asked by Pragnya Kar | 29th Sep, 2014, 11:18: PM

Expert Answer:

The seven fundamental or base quantities chosen in SI units are the seven dimensions. They are denoted within square brackets[ ] .
Length is represented by [L], mass by [M] time by [T] ,electric current by [A] temperature by [K], luminous intensity by [Cd]
and amount of substance by [mol].
The dimensions of a physical quantity are the powers or exponents to which the units of base quantities are raised to represent a derived unit of that quantity.
All physical quantities can be represented in terms of the dimensions of length[L] , mass[M], and time[T]
 
Example: Area = length × breadth = L× L
Dimensional formula = [L]2
Thus to represent area we have to raise [L] to the power 2. Therefore Area is said to have two dimensions in length . As unit of mass and time are not required in representing area , we can write the dimensional formula of area as: [M0L2T0] and hence we say that area has zero dimension in mass and time in addition to 2 dimensions in length.
Similarly Velocity =displacement / Time
                        =[L] / [T]
Velocity =[LT-1] =[M0L1T-1]. This is the dimensional formula of velocity
The dimensions of velocity are : zero in mass. +1 in length and -1 in time.
To find the dimensions :
First the relation of the physical quantity with respect to other quantities have to be known, like density = mass/ volume. And then its written in terms of the dimensions of the fundamental quantities .In such a way you can find the dimensions of any physical quantity. 

Answered by Jyothi Nair | 30th Sep, 2014, 10:50: AM