Density is a measure of how much mass is present in a given volume. It is typically represented by the symbol “ρ” (rho) and is calculated by dividing the mass of an object by its volume.

The dimensional formula for density is therefore represented as follows:

**[ M**^{1}** L**^{-3}** ]**

where [M] represents the dimension of mass and [L] represents the dimension of length.

## Derivation of Dimensional Formula of Energy

We know that the formula of density is

Density = Mass / Volume

In order to calculate the dimensional formula of density, we need to determine the dimensions of mass and the dimensions of volume.

The dimensions of mass are typically represented by the symbol “M”, and the dimensions of length are typically represented by the symbol “L”.

Now, we know that volume is represented by the length raised to power 3 (L^{3}). Therefore, the dimensional formula for density is calculated as follows:

**Density = Mass / (Length * Length * Length)**

Substituting the value of Mass and Length with their dimensional symbol.

**Density = [M] / ([L] * [L] * [L])**

**Density = [M] / [L ^{3}]**

**Dimensional Formula of Density = [ M L ^{-3} ]**

In conclusion, the dimensional formula for density is the ratio of mass dimensions to volume dimensions. This formula is important for understanding the relationship between mass, volume, and density.

## Calculate Dimensional Formula of Density Using Units

We can also calculate the dimensional formula of density using the units of mass and volume.

We typically use units of grams (g) or kilograms (kg) as a measurement for Mass, while for volume, we use units of cubic meters (m^3), cubic centimeters (cm^3), or milliliters (mL).

For example, the density of water is about 1 g/cm^3 or 1 kg/L. This means that for every cubic centimeter of water, there is a mass of 1 gram, or for every liter of water, there is a mass of 1 kilogram.

**Density = Mass / Volume**

Substituting the units of mass and volume,

**Density = kilogram / length**** = kg / l ^{3} = kg l^{-3}**

Dimensionally, we use M to represent kilogram and l to represent length. Hence, the dimensional formula of density will be **[ M L**^{-3}** ]**.

**Note:** When calculating density, it is important to ensure that the units of mass and volume are consistent. For example, if we are using the unit grams for the mass of an object, then we should use cubic centimeters for the volume. Hence, the resulting density will be in units of grams per cubic centimeter.

## Frequently Asked Questions

### 1. What is the dimensional symbol of density?

The dimensional symbol of density is **[ M L**^{-3}** ]**.

### 2. What is the dimension of linear density?

The dimension of linear density is **[ M L**^{-1}** ]**.