CBSE Tutorials

Floatation–Density and Relative Density | Class 9

Density

We describe the lightness or heaviness of different substances by using the word density.

The density of a substance is defined as mass of the substance per unit volume. That is

\displaystyle \mathbf{Distance}=\frac{\mathbf{mass}\,\,\mathbf{of}\,\,\mathbf{the}\,\,\mathbf{substance}}{\mathbf{vol}\mathbf{.}\,\,\mathbf{of}\,\,\mathbf{the}\,\,\mathbf{substance}}

\displaystyle \mathbf{8}\mathbf{.9}\,\mathbf{unit}\to \mathbf{kg/}{{\mathbf{m}}^{\mathbf{3}}}\,\,\,\mathbf{or}\,\,\,\,\mathbf{kg}\,{{\mathbf{m}}^{-\mathbf{3}}}

The density of a given substance, under specified conditions remains the same. The therefore the density of a substance is one of the characteristic property of a substance.

For example, density of gold is \displaystyle \mathbf{19300}\,\mathbf{kg/}{{\mathbf{m}}^{\mathbf{3}}} while that of water is \displaystyle 10\mathbf{00}\,\mathbf{kg/}{{\mathbf{m}}^{\mathbf{3}}}.

The density of a given sample of a substance can help us to determine its purity.

Relative Density

The relative density of a substance is the ratio of its density to that of water.

Relative density of a substance \displaystyle =\frac{\mathbf{Density}\,\,\mathbf{of}\,\,\mathbf{the}\,\,\mathbf{substance}}{\mathbf{Density}\,\,\mathbf{of}\,\,\mathbf{water}}

Since the relative density is a ratio of similar quantities, it has no unit.

The relative density of a substance expresses the heaviness of the substance in comparison to water. For example the relative density of iron is 7.8. This means that iron is 7.8 times as heavy as an equal vol. of water.

The relative density of water is 1. Now if the relative density of a substance is more than 1, then it will be heavier than water and hence it will sink in water. On the other hand if the relative density of a substance is less than 1, it will be lighter than water and hence float in water.

Question: The mass of 2 m3 of steel is 15600 kg. Calculate the density of steel is S.I. Units.

Solution: We know that density \displaystyle =\frac{\mathbf{mass}}{\mathbf{volume}}

\displaystyle =\frac{15600\,kg}{2{{m}^{2}}} \displaystyle =7800\,kg/{{m}^{3}}

Question: An object of mass 50 kg has a vol. of 20 m3. Calculate the density of the object. If the density of water be \displaystyle 1\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}. State whether the object will float or sink is water

Solution: Density \displaystyle =\frac{\mathbf{mass}}{\mathbf{volume}}

Mass of the object = 50 g

Volume of the object = \displaystyle 20\,\,\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}

Density \displaystyle =\frac{50\,g}{20\,c{{m}^{3}}}=2.5\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}

Question: The relative density of silver is 10.8. If the density of water be \displaystyle 1\times {{10}^{3}}\,\mathbf{kg/}{{\mathbf{m}}^{\mathbf{3}}}. Calculate the density of silver is S.I. Units.

Solution: Relative Density \displaystyle =\frac{\mathbf{Density}\,\,\mathbf{of}\,\,\mathbf{the}\,\,\mathbf{substance}}{\mathbf{Density}\,\mathbf{of}\,\mathbf{water}}

Relative density of silver = 10.8

Density of silver = ?

Density or eater \displaystyle =1\times {{10}^{3}}\,\,\mathbf{kg/}\,{{\mathbf{m}}^{\mathbf{3}}}

\displaystyle 10.8=\frac{\mathbf{Density}\,\,\mathbf{of}\,\,\mathbf{silver}}{1\times {{10}^{3}}}

Density of silver \displaystyle =10.8\times {{10}^{3}}\,\,\mathbf{kg/}{{\mathbf{m}}^{\mathbf{3}}}

Question: The volume of a solid mass 500g is \displaystyle \mathbf{350}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}

(a) What will be the density of this solid?

(b) What will be the mass of water displaced by this solid?

(c) What will be the relative density of the solid?

(d) Will it float or sink in water?

Solution: (a) Density \displaystyle =\frac{\mathbf{Mass}}{\mathbf{Volume}} \displaystyle =\frac{500}{350}\,\,\,\,=1.42\,\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}

(b) The solid will displace water equal to its an volume. Since the volume of solid is \displaystyle \mathbf{350}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}} so it will displace \displaystyle \mathbf{350}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}of water. Now vol. of water displaced is \displaystyle \mathbf{350}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}} and the density of water is \displaystyle \mathbf{1}\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}.

Density of water \displaystyle =\frac{mass\,of\,water}{volume\,of\,water}

\displaystyle \mathbf{1}\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}=\frac{\mathbf{mass}\,\mathbf{of}\,\mathbf{water}}{\mathbf{350}\,\,\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}}

Mass of water \displaystyle =\mathbf{1}\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}\times \mathbf{350}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}} \displaystyle =350\,\mathbf{g}

(c) \displaystyle \mathbf{R}\mathbf{.D}\mathbf{.}=\frac{\mathbf{Density}\,\,\mathbf{of}\,\,\mathbf{solid}}{\mathbf{Density}\,\,\mathbf{of}\,\,\mathbf{water}}=\frac{\mathbf{1}\mathbf{.42}\,\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}}{\mathbf{1}\,\,\mathbf{g/c}{{\mathbf{m}}^{\mathbf{3}}}}=\mathbf{1}\mathbf{.42}

Since the R.D. of this solid is greater than R. D. of water i.e., 1 therefore this solid is heavier than water and hence it will sink in water.

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