# Dimensional Formula of Work

The dimensional formula of Work is

[ M1  L2  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 / time2

Therefore,

``````
Work = ( mass * distance / time2 ) * displacement

Work = ( mass * distance * displacement ) / time2

Work = mass1 * distance1 * displacement1 * time-2``````

Dimensionally, we use

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

Now the formula becomes

``````
Work = [M1] * [L1] * [L1] * [T-2]

Work = [M1] * [L2] * [T-2]
``````

Hence, the dimensional formula of work becomes [ M1 L2 T-2 ].

Related Articles