Dimensions of a Physical Quantity Physics Notes

Dimensions of a Physical Quantity:

The dimensions of a physical quantity is defined as the powers to which the fundamental quantities are raised in order to represent that physical quantity.
The seven fundamental quantities are denoted with square brackets [ ].

For example length is represnted by [L], mass by [M], the dimension of time is described as [T], electric current by [A] and so on.

Consider a physical quantity Q which depends on base quantities like mass, length, time, electric current, the amount of substance and temperature, when they are raised to power a, b, c, d, e and f.Then dimensions of physical quantity Q can be given as:

[Q] = [M^a L^b T^c A^d mol^e k^f]

It is mandatory for us to use [ ] in order to write the dimension of a physical quantity. Look out few examples given below:

1. The volume of a solid is given as the product of length, breadth, and its height. Its dimension is given as:
Volume = Length × Breadth × Height
Volume = [L] × [L] × [L] (as length, breadth 8 heights are length]
Volume = [L]³

As volume does not depend on mass and time, so the power of mass and time will be zero while expressing its dimensions.
The final dimension of volume will be [M]0{L]3|T]0
= [M⁰L³T⁰]

2. Velocity = \(\frac{\text { displacement }}{\text { time }}\)
v = \(\frac{\text { [L] }{\text { [T] }}\) = [M⁰ L^-1 T^-1]
Dimension of velocity are 0 in mass, 1 in length and -1 in time i. e., (0, 1, -1).

3 Acceleration = \(\frac{\text { changein velocity }}{\text { timetaken }}\)
= \(\frac{\text { displacement }}{\text { time } \times \text { time }}\)
a = \(\frac{\left[\mathrm{L}^{1}\right]}{\left[\mathrm{T}^{2}\right]}\)
Dimensions of acceleration are (0, 1, – 2).

4. Force:
F = mass × acceleration
= [M¹] × [M⁰ L¹ T^-2]
= [M¹ L¹ T^-2 ]
dimensions of force are (1, 1, – 2).
Note: In dimensional representation, the magnitudes are not considered.