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What is the dimensional formula of density with solution?

Published in Physics 1 min read

The dimensional formula of density is [ML⁻³]. Here's how we derive it:

Density is defined as mass per unit volume. To determine its dimensional formula, we need to express mass and volume in terms of their fundamental dimensions:

  • Mass (M): The fundamental dimension of mass is simply [M].

  • Volume (V): Volume is length cubed (length × length × length). Therefore, the dimensional formula for volume is [L³].

Now, we can express density as:

Density = Mass / Volume

Dimensional Formula of Density = [M] / [L³] = [ML⁻³]

In summary:

  • Density: Mass / Volume
  • Dimensional Formula of Mass: [M]
  • Dimensional Formula of Volume: [L³]
  • Dimensional Formula of Density: [ML⁻³]

This shows that density has a dimension of mass and a dimension of length to the power of -3.