Dimensional Formula of Density

The mass of a material substance per unit volume is known as density. Each substance has a distinct density, which is determined by how the material’s particles are packed together. More particles can fit into a given volume if the particles of a substance are kept neatly and closely together. Because particles have mass, the more particles you can cram into a given volume, the heavier the substance.

Density can be formulated as:

Density = mass/volume

where mass is the amount of matter a substance contains and its unit is kg

And volume is the amount of space an object occupies and its unit is m3

Thus its S.I. unit is kg/m³.

The dimension formula is a collection of fundamental quantities generated from physical quantities derived units. Square brackets are used to symbolise it. The dimensional formulae of fundamental quantities like mass, time and length can be written as [M], [T] and [L] respectively.

For finding the dimensional formula of density, its formula can be simplified using the basic fundamental quantities.

Dimensional Formula:

In terms of dimensions, a dimensional formula is an equation that expresses the relationship between fundamental and derived units (equation). The letters L, M, and T are used to represent the three basic dimensions of length, mass, and time in mechanics.

All physical quantities can be stated in terms of the fundamental (base) units of length, mass, and time, multiplied by some factor (exponent).

The dimension of the amount in that base is the exponent of a base quantity that enters into the expression.

The units of fundamental quantities are expressed as follows to determine the dimensions of physical quantities:

• ‘L’ stands for length,

• ‘M’ for mass, and

• ‘T’ for time.

Example: The area is equal to the sum of two lengths. As a result, [A] = [L2]. That is, an area has two dimensions of length and zero dimensions of mass and time. In the same way, the volume is the sum of three lengths. As a result, [V] = [L³]. That is, the volume dimension has three dimensions: length, mass, and time.

The Dimensional Formula of any bodily amount is defined as the expression that represents how and which of the bottom portions are protected in that amount. It is denoted through enclosing the symbols for base portions with suitable strength in rectangular brackets i.e [ ]

Derivation of the dimensional formula of density:

In order to find the dimensional formula of density, substitute the fundamental dimensional formulae of mass and volume in the formula of density.

The fundamental dimensional formula of mass is [M] and the dimensional formula of volume is [L³].

So,

Density = mass/volume

Density = [M1][L3]

Using negative exponents rule,

Density = [M¹][L^-3]

Combining the two quantities

Density = [M¹L^-3]

So, the dimensional formula of density is [M¹L^-3].

Conclusion :

Density is defined as the mass of a material substance per unit volume. The dimension formula is a set of fundamental quantities that are derived from physical quantities. The three basic dimensions of mechanics are mass, length, and time. Fundamental dimensional quantities are the dimensional equations of these fundamental quantities. They are denoted by the letters [M], [L], and [T], respectively. Substitute the fundamental dimensional equations of mass and volume in the formula of density to derive the dimensional formula of density. As a result, the density dimensional formula is [M¹L^-3].