What is the dimension of Force?

The dimensional formula of force isĀ 

[ M1 L1 T-2 ]

where, [M], [L], and [T] represent fundamental quantity Mass, Length, and Time.

From this formula, we can say that the dimension of force is 1, 1, and -2 in terms of fundamental quantities Mass, Length, and Time.

Now, let’s see how we can derive this formula.


Derivation: Dimension Formula of Force

For this derivation, we need to revise some of the basic physics formulas.

QuantityFormula
Force (F)Mass (m) * Acceleration (a)
Acceleration (a) Velocity (v) / Time (T)
Velocity (v)Displacement (D) / Time (T)

Now, let’s use these formulas to find the dimension of the force.


Force    =   Mass * Acceleration

         =   Mass * (Velocity / Time)     [using formula of acceleration]

         =   Mass * (Displacement / (Time * Time) )   [using formula of velocity]

         =   ( Mass * Displacement ) / Time2

         =   Mass1 * Displacement1 * Time-2

We know that dimensionally, we use [M] for mass [L] for displacement, and [T] for time.

With this in mind, our dimensional formula of force becomes

Force = [ M1  L1  T-2 ]

And finally,

Dimensions of Force = 1, 1, -2

The dimensions of force is 1, 1, -2 in terms of Mass, Length and Time.
Visual derivation of the dimensional formula of Force

1. How to find the SI unit of Force using the dimensional formula?

We know that the dimensional formula of force is [ M1  L1  T-2 ]. Now, let’s derive the unit from it.

The unit for 

  • [M], Mass is kg (kilogram)
  • [L], length is m (meter)
  • [T], time is s (second)

Now if we use these units for respective physical quantity,

Unit of Force = kg1 m1 s-2  = kg m s-2


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