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).
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 / 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 ].

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