### Direct method | Regular Solids:

Density is defined as mass per unit volume. The unity of density in metric units is kg/m^{3}.

The symbol for density is the Greek letter rho, \( \scriptsize (\rho) \)

Mathematically, it is given as:

**Density** = \( \frac{mass (m)}{volume (v)} \)

i.e \(\scriptsize \rho = \normalsize \frac{mass (m)}{volume (v)} \)

**Mass (m)** = \( \scriptsize density \: (\rho) \: \times \: volume \: (v) \)

i.e m = \( \scriptsize \rho \: \times \: v \)

and;

**Volume (v)** = \( \frac{mass (m)}{density (\rho)} \)

i.e v = \( \frac{m}{\rho} \)

If the mass is expressed in gm and the volume in cm^{3}, then the unit of density is gm/cm^{3}. The mass of a regular object is determined by using a suitable weighing balance and the dimensions of the regular object are measured to determine its volume.

### Irregular Solids:

The mass of an irregular solid body can be obtained by direct weighing. The volume of an irregular solid is found by immersing the solid in water, provided it will not sink. The volume of water displaced will be equal to the volume of the solid. A measuring cylinder or an overflow can be used in determining the volume of the liquid displaced. Knowing the volume and the mass of the irregular solid (applicable only to objects, which sink in water), the density of the solid can be determined.

### Relative Density and its Determination:

**Relative density: **Since water is the most common substance and its density is 1000kg/m^{3} or 1gm/cm^{3}, it is easy to use it as a standard for comparing the densities of other substances. The relative density of any substance is defined as follows:

Relative density = \( \frac {density \: of \: substance} {mass \: of \: equal \:volume \: of \: water } \)

Relative density has no units. Relative density is sometimes known as specific gravity.

**Density bottle method:** A relative density bottle can be used to find the density of liquid directly:

**(a) **The density bottle is weighed when empty, say of mass m

**(b) **It is then filled with liquid and weighed, as mass m_{1}

**(c) **Finally, it is emptied, dried, and refilled with water again, as mass m_{2}

Mass of liquid in the body = m_{1} â€“ m

Mass of water in the bottle, occupying the same volume as liquid (m_{2} â€“ m_{1})

Therefore, using relative density:

Relative density = \( \frac{m_1 \; – \; m}{m_2 \: – \: m_1} \)

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