A solid of mass 400g in air and when partly is immersed in a certain liquid it has a mass 320g. Given that the relative density is 0.8. Calculate the volume of the solid immersed in the liquid.
To calculate the volume of the solid immersed in the liquid, we need to first understand the concept of relative density.
Relative density is defined as the ratio between the density of a substance and the density of a reference substance. In this case, the reference substance is usually water. Relative density is also known as specific gravity.
The formula for relative density is:
Relative Density = Density of Substance / Density of Reference Substance
In this question, the relative density is given as 0.8. This means that the density of the solid is 0.8 times the density of the liquid.
To find the volume of the solid immersed in the liquid, we can start by finding the density of the solid.
Density is calculated using the formula:
Density = Mass / Volume
We are given that the mass of the solid is 400g in air and when partly immersed in the liquid it has a mass of 320g. We can subtract the mass of the solid in air from the mass of the partially immersed solid to find the mass of the liquid displaced:
Mass of Liquid Displaced = Mass of Solid in Air - Mass of Partially Immersed Solid
Mass of Liquid Displaced = 400g - 320g
Mass of Liquid Displaced = 80g
Now we can find the volume of the liquid displaced using the definition of density:
Density = Mass / Volume
Since we know the mass of the liquid displaced is 80g, and the relative density is 0.8, we can rearrange the formula to solve for volume:
Volume = Mass of Liquid Displaced / (Relative Density x Density of Reference Substance)
The density of water (the reference substance) is commonly known to be 1g/cm³.
Plugging in the values:
Volume = 80g / (0.8 x 1g/cm³)
Volume = 80cm³ / 0.8
Volume = 100cm³
Therefore, the volume of the solid immersed in the liquid is 100cm³.