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 ].
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