The ratio of the mass of an object to its unit volume is known as density.

⍴= M/V

Where ⍴= density of the substance

M= mass of the substance

V= volume of the substance

Density is measured in Kilogram per metre cube or Kg/m3, which is its S.I. unit. The symbol of density is rho (⍴).

The ratio of the density of a material to the density of reference material is known as its relative density, also known as specific density. For most liquids, the relative density is calculated with respect to the density of water.

Relative density = Density of a material/ Density of reference material

To measure the density of regular solids, find the mass of the regular solid. You can use a beam balance to know the mass.

Calculate the volume of the solid using the prescribed formulas. Some common shapes and their volumes are given by –

• The volume of a cube = Cube of measure of a side
• Volume of a cuboid = Length x breadth x height
• Volume of a cylinder = 4/3 x pi x cube of radius
• Volume of sphere = 4 x pi x cube of radius
• The volume of cylinder = pi x square of radius x height

Using the values of mass and volume, find the density of the solid by

Density = mass/ volume

To find the measurement of the density of irregular solids, we must first determine their mass and volume.

Using a physical balance, we can find the mass of an irregular solid. To find the volume of an irregular solid, we can’t use any pre-described formulas. We use a different approach here using the concept of volume that states that the amount of space taken by an object is its volume.

First, we take a cylinder or any other container that has markings for volume. Then, fill this container with water and note the initial reading. Next, we dip the object in this water, increasing the container’s water level. This elevated water reading is noted in the final reading. The difference between the two markings will give us the object’s volume, which has an irregular shape.

After we determine the mass and volume of the irregular solid, the density is given by

D = mass/volume

A specially designed bottle, known as the density bottle, is used for measurement of the density of fluids.

• First, we find the mass of the bottle with the help of a balance. Next, we fill this bottle with water and again measure its mass.
• Then, we empty all the water from this bottle.
• We fill the emptied and dried bottle with the liquid whose density we want to find.
• Next, we measure the mass of the liquid-filled density bottle.
• Using these measurements, we first find the mass of water.

Mass of water = mass of bottle filled with water – the mass of the empty bottle

Mass of liquid = mass of bottle filled with liquid – the mass of the empty bottle

• Now, we know that the density of water is 1gm/cm3. So, the value of the mass of water in the volume is the same as the volume of the density bottle.
• Therefore, the density of the liquid = mass of liquid/ mass of water.

The Law of Floatation states that “The weight of the solid floating in a fluid is equal to the weight of the fluid displaced by immersed part of the solid.”

Let us understand the concept of floatation and sinking of a substance. An object with its relative density with water less than one floats on the surface of the water, while an object with a relative density of more than one sinks when placed in water. So, floatation and sinking depend upon the relation between the density of water and the object’s density.

Two forces act on an object when it is immersed in a liquid:

• The first force ties to make the object sink in the liquid. It is the weight of the body that acts perpendicularly downwards.
• The second force is the buoyant force that acts vertically upwards. The buoyant force is equal to the liquid’s weight that the object has displaced when immersed in the liquid.
• So, the volume of an object x density of an object = Volume of the displaced liquid x density of the liquid.

The three states of matter, i.e., solid, liquid, and gas, possess different properties. The molecular placement in the three states of matter is different and so are their intermolecular spaces. The densities of these states of matter also differ according to the arrangement of their molecules.

The comparison of densities in the three states of matter is given below:

The measurement of density helps us understand the process of sinking and floatation. To compare the different physical quantities, we use measurement expressed in the form of units. The physical quantities and measurements are essential to apply the concepts of physics in the real world.

1. What is the unit of relative density?
   Since relative density is the ratio of an object’s density with respect to reference material, it is a dimensionless quantity.
2. What device is used for the measurement of the density of fluids?
   A density bottle is used to measure the density of fluids.
3. What is buoyancy?
   The buoyancy of an object is its virtue of floating on the liquid’s surface.