## Dimensional Formula of Force with its Derivation

In this article, we will find the dimension of Force

Dimensional formula for is

$[M^1L^1T^{-2}]$

Where**M** -> Mass

**L** -> Length

**T** -> Time

We would now derive this dimensional formula.

### Derivation for expression of Dimension of

As per second laws of Newton law’s, Force is defined as the product of mass and acceleration

$F= ma$

Where m -> Mass of the body

a -> Acceleration of the body

Now the dimension of Mass = $[M^1]$

Lets derive the dimension of Acceleration

Now

$a = \frac {\Delta v}{t}$

Now dimension of Velocity= $[M^0 L^1T^{-1}]$

dimension of Time = $[M^0 T^1]$

So dimension of Acceleration = $ \frac {[M^0 L^1T^{-1}]}{ [M^0 T^1]}= [M^0 L^1T^{-2}]$

Hence Dimension of force is given by

$\text {Dimension of Force} =[M^1] \times [M^0 L^1T^{-2}] = [M^1L^1T^{-2}]$

Unit of Force is Newton

Try the free Quiz given below to check your knowledge of Dimension Analysis:-

**Quiz on Dimensional Analysis**

**Related Articles and references**

- Newton’s Law of Motion
- Newton’s Second Law of Motion
- Dimensional Analysis:- a very good website for physics concepts
- Dimensional Formula of Spring constant
- dimension of Density
- dimension of frequency

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