In our example, the specific gravity of the stone with its known mass will also determine its volume, by which we can calculate the buoyancy force of water acting on the stone.
The specific density of stone (natural) has a wide range (from 1100 kg / m³ to 2700 kg / m³). For convenience, we will take the specific density of the stone for 2000 kg / m³.
Then the volume of our stone will be, according to a simple formula connecting density (ρ), mass (m) and volume of a body (V), –
V = m / ρ –
0.2 kg / 2000 kg / m³ = 0.0001 m³.
The buoyancy force acting on a body immersed in a liquid is equal to the weight of the liquid displaced by it, or, in other words, the weight of the liquid that fills the volume occupied by the body immersed in the liquid.
F ext = Vρg, where V is the volume of the body, ρ is the density of the liquid (in our case, water – 1000 kg / m³), g is the acceleration of gravity (let’s round its value to 10 m / s²).
Substituting the values we know, we get the following equation –
F ext = 0.0001 m³ * 1000 kg / m³ * 10 m / s² = 1 N. So, the buoyancy force we are looking for, acting on the stone, according to the conditions of our example, will be equal to 1 Newton.