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