**Dimensional Formula of Work**

**with its Derivation**

In this article, we will find the dimension of Work Done

Dimensional formula for Work done is

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

Where

**M** -> Mass

**L** -> Length

**T** -> Time

We would now derive this dimensional formula.

### Derivation for expression of Dimension of Work

Work is defined as the cross product for Force and displacement

$W= F.d$

Where d -> displacement

F -> Force applied

W-> Work done by the Force

So,

Now the dimension of displacement= $[L^1]$

Lets derive the dimension of Force

$F= ma$

Now

Where m-> mass

a -> Acceleration

Dimension of Mass = $[M^1]$

Now acceleration

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

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}]$

So, Dimension of force is given by

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

Now we know both the displacement and Force dimension , we can calculate the dimension of Work easily as

$\text {dimension of Work} = \text {dimension of Force} \times \text {dimension of displacement}$

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

Unit of Work Done is Joule.

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

**Quiz on Dimensional Analysis**

**Related Articles**

- Dimensional Analysis:- a very good website for physics concepts
- Work Done Formula
- Work done by Variable Force

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