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).


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 ].

Derivation of dimensional formula of work

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