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Density Formula

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  • Last Updated : 31 Mar, 2022
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In physics and engineering, density is a fundamental and basic notion. Archimedes, a Greek scientist, was the first to discover density. It also has a significant link to an object’s mass. Furthermore, this measurement is necessary for determining whether or not anything will float on the surface of a fluid. One of the most crucial characteristics of an object is its density. Here’s how to calculate density.

Density

The mass of a substance per unit of volume is measured by density. A pure substance’s mass concentration and this measurement have the same value. Various materials or substances have varying densities. Furthermore, the purity, buoyancy, and packing of the material may all be affected by this measurement.

The comparisons of this measurement across multiple units systems can be made easier. It is possible that this measurement will be replaced with a concept called relative density. The density of a substance in relation to that of a standard substance or material, usually water, is referred to as relative density.

MetalsDensity (mg/m3)
Titanium4.50
Barium3.50
Scandium2.99
Magnesium1.74

The units used are g/cm3 for solids, g/ml for liquids, and g/L for gases instead of the SI unit of density, which is kg/m3. The D can also be used to signify density, which is represented by the symbol ρ.

Formula of Density

Density formula is as follows,

ρ = m/V

Where,

  • ρ = Density,
  • m = mass,
  • V = volume.

Real life application of Density

Separation strategies benefit from understanding the densities of two substances. Separating oil from water, for instance. When an oil tank leaks into the ocean, the oil drops float because of their lower density in the water.

Sample Questions

Question 1: What method would you use to determine the density of a human body?

Answer:

The expression below can be used to calculate the density of a human body,

Density = mass/volume

A weight scale can be used to determine the mass of the human body. To calculate the volume of the human body, submersion displacement is used. We may witness a rise in the water if we fill a tub with water and totally submerge a person in it. This increase is equivalent to the volume of the body. By dividing the mass of the human body by the volume of the human body, the density of the human body may be determined.

Question 2: Who was the first to develop the density principle?

Answer:

Archimedes, a Greek scientist, was the first to discover density. Earlier scientist decided to divide the mass of any object with its volume to obtain a certain parameter, this is how the concept of density evolved around 250 BC. 

Question 3: If water has a mass of 934 kg and a volume of 6 m3, what is its density?

Solution:

Given: m = 934 kg, V = 6 m3

Since,

ρ = m/V

∴ ρ = 934/6

∴ ρ = 155.6 kg/m3

Question 4: You’re preparing to travel to Mars. You’ve been given a 1.34-meter-long cubical box to pack. Your box’s final density must be no more than 5 kg/m3 due to fuel and space constraints. What is the maximum weight you can carry?

Solution:

Given: V = 1.34 m × 1.34 m × 1.34 m = 2.4061 m3, ρ = 5 kg/m3

Since,

ρ = m/V

∴ m = ρ × V

∴ m = 5 × 2.4061

∴ m = 12.0305 kg ≅ 12 kg

Question 5: Is it graphite or diamond if you locate a gleaming rock, a carbon allotrope with a volume of 0.173 cm3 and a mass of 0.14 g? Graphite has a density of 2.266 g/cm3, while diamond has a density of 3.51 g/cm3.

Solution:

Given: V = 0.173 cm3, mass of gleaming rock = 0.20 g, density of graphite = 0.74 g/cm3, density of diamond = 4.28 g/cm3

Since,

ρ = m/V

∴ m = ρ × V

∴ mass of graphite = 3.17 × 0.173 = 0.548 g

∴ mass of diamond = 4.28 × 0.173 = 0.740 g

Mass of gleaming rock is same as mass of diamond.

Question 6: What is the density of a sugar cube that weighs 30 grams and has a side length of 8 cm?

Solution:

Given: m = 30 g, V = 8 cm × 8 cm × 8 cm = 512 cm3.

Since,

ρ = m/V

∴ ρ = 30/512

∴ ρ = 0.0585 g/cm3

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