# 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: [M^{0}L^{2}T^{0}] 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}] =[M^{0}L^{1}T^{-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.

^{2}

^{0}L

^{2}T

^{0}] and hence we say that area has zero dimension in mass and time in addition to 2 dimensions in length.

^{-1}] =[M

^{0}L

^{1}T

^{-1}]. This is the dimensional formula of velocity

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

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