Relative density of a substance

1. If R.D > 1: the substance is denser than water (it will sink).
2. If R.D < 1: the substance is less dense than water (it will float).
3. If R.D = 1: the substance has the same density as water.

Example 1

An object has a density of 7 g/cm³. Calculate its relative density.

Solution:

$\text{R.D} = \frac{7 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} = 7$

Therefore, the relative density of the object is 7.

Example 2

A piece of copper metal has a volume of 5.1 cm³ and a mass of 41.6 g. Find the relative density of copper.

Solution:

$\text{Density} = \frac{41.6 \, \text{g}}{5.1 \, \text{cm}^3} = 8.16 \, \text{g/cm}^3$

$\text{R.D} = \frac{8.16 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} = 8.16$

So, the relative density of copper is 8.16.

Aim: to find the relative density of a solid material.

Apparatus: Eureka can, measuring cylinder, beaker, water, string, beam balance, solid object.

Procedure:

1. Measure the mass $m_0$ of the solid using a beam balance.
2. Fill the Eureka can with water until it starts overflowing through the spout.
3. Place a dry beaker of mass $m_1$ under the spout.
4. Lower the solid into the can using a string, so it is fully submerged.
5. Collect the overflowing water into the beaker.
6. Measure the mass $m_2$ of the beaker with water.

Calculations:

• Mass of equal volume of water: $m_2 - m_1$

• Relative density:

  $\text{R.D} = \frac{m_0}{m_2 - m_1}$

Example 3

A metal block weighs 264 g. It displaces 24 g of water when submerged in a Eureka can. Calculate its relative density.

Solution:

$\text{R.D} = \frac{264 \, \text{g}}{24 \, \text{g}} = 11$

The relative density of the metal block is 11.

Aim: to find the relative density of a liquid.

Apparatus: relative density bottle, cooking oil (or any liquid), water, beam balance.

Procedure:

1. Measure the mass $m_0$ of the empty bottle with stopper.
2. Fill the bottle with the liquid. Measure the new mass $m_1$.
3. Empty, clean, and dry the bottle.
4. Fill it with water. Measure the mass again as $m_2$.

Calculations:

• Mass of liquid: $m_1 - m_0$

• Mass of equal volume of water: $m_2 - m_0$

• Relative density:

  $\text{R.D} = \frac{m_1 - m_0}{m_2 - m_0}$

Note: the bottle has a narrow hole in the stopper to allow air to escape while filling, ensuring accurate volume.

Example 4

In an experiment:

• Mass of empty bottle = 15 g
• Mass with liquid X = 35 g
• Mass with water = 40 g
• Volume = 25 cm³

(a) Density of water (kg/m³):

$\text{Density} = \frac{25 \, \text{g}}{25 \, \text{cm}^3} = 1 \, \text{g/cm}^3 = 1000 \, \text{kg/m}^3$

(b) Density of liquid X (kg/m³):

$\text{Density} = \frac{20 \, \text{g}}{25 \, \text{cm}^3} = 0.8 \, \text{g/cm}^3 = 800 \, \text{kg/m}^3$

(c) Relative density:

$\text{R.D} = \frac{800}{1000} = 0.8$