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)**.

## How to calculate the 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}** ]**.

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