You find the dimension of density by expressing it in terms of the fundamental dimensions of mass, length, and time.
Here's how you determine the dimensional formula for density:
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Recall the definition of density: Density (ρ) is defined as mass (m) per unit volume (V): ρ = m/V
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Identify the fundamental dimensions of mass and volume:
- Mass (m) has the fundamental dimension of [M].
- Volume (V) is a measure of length cubed (length x width x height), so it has the fundamental dimension of [L³].
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Substitute the dimensions into the density formula: ρ = m/V becomes [ρ] = [M] / [L³]
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Express the dimensional formula: [ρ] = [ML⁻³]
Therefore, the dimension of density is mass divided by length cubed, represented as [ML⁻³]. This means density has a dimension of 1 in mass and -3 in length. Time is not a factor in the dimension of density.
