The dimensional formula of Work is

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

where **[M]**, **[L]** and **[T]** are the fundamental quantities: **Mass**, **Length**, and **Time**.

From the above formula, we can derive the **dimensions of work as (1, 2, -1)**.

## Derivation of Dimensional Formula of Work

We can derive this formula using the definition of work.

In physics, we can define work done as the total force applied to move a body. So, mathematically, work is given as:

```
Work = Force * displacement
```

We know that **Force = mass * acceleration**. Substituting the value of **Force** in the above formula, we get

```
Work = mass * acceleration * displacement
```

We know

- acceleration = speed / time
- speed = distance / time
- acceleration = distance / time
^{2}

Therefore,

```
Work = ( mass * distance / time
```^{2} ) * displacement
Work = ( mass * distance * displacement ) / time^{2}
Work = mass^{1} * distance^{1} * displacement^{1} * time^{-2}

Dimensionally, we use

**[M]**for mass**[L]**for distance and displacement**[T]**for time

Now the formula becomes

```
Work = [M
```^{1}] * [L^{1}] * [L^{1}] * [T^{-2}]
Work = [M^{1}] * [L^{2}] * [T^{-2}]

Hence, the **dimensional formula of work becomes [ M**^{1}** L**^{2}** T**^{-2}** ]**.

**Related Articles**