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## Dimensions

Each base quantity is considered a dimension denoted by a specific symbol written within square brackets. It stands for the qualitative nature of the physical quantity. For example, different quantities such as length, breadth, diameter, light year which are measured in metre denote the same dimension and have the dimension of length [L]. Similarly the mass and time dimensions are denoted by [M] and [T], respectively. Other quantities that we measure have dimension which are combinations of these dimensions. For example, speed is measured in meters per second. This will obviously have the dimensions of length divided by time. Hence we can write.

Dimensions of speed = Dimension of distance / Dimension of time

Dimensions of speed = [L] / [T]

[V] = = [L] [Tˉ¹] = [LTˉ¹]
Similarly the dimensions of acceleration are
[a] = [L] [Tˉ²] = [LTˉ²]
And that of force are
[F] = [m] [a] = [M] [LTˉ²] = [MLTˉ²]
Using the method of dimensions called the dimensional analysis; we can check the correctness of a given formula or an equation and can also derive it. Dimensional analysis makes use of the fact that expression of the dimensions can be manipulated as algebraic quantities.

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