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Density And Relative Density

Concept Explanation

Relative Density

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

Relative density of a substance = $large frac{Density;of;the;substance}{Density;of;water}$

In other words, we can say that,

Relative density of a substace $large =frac{Mass;of;the;substance}{Volume;of;the;substance}timesfrac{Volume;of;water}{Mass;of;water}$

$large left [ because density=frac{mass}{volume} right ]$

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

The relative density of a substance expresses the heaviness (or density) of the substance in comparison to water. By saying that relative density of iron is 8.7, we mean that iron is 8.7 times heavy as an equal volume of water.

Note Density of water is $large 1000;kg;m^{-3};or;1g;cm^{-3}$

The relative density of a substance is found accurately by using Archimedes principle.

Example: A solid of mass 600 g has volume $large 450;cm^{3}$ . Then,

(i) what is the density of this solid?

(ii) what will be the mass of water displaced by this solid?

(iii) find the relative density of the solid.

(iv) will it float or sink in water?

Solution: Given, mass of solid, m = 600 g

Volume of solid, $large V=450;cm^{3}$

(i) $large therefore$ Density of solid $large =frac{Mass}{Volume}=frac{600}{450}$

$large =1.33;g;cm^{-3}$

Therefore, density of solid = $large =1.33;g;cm^{-3}$

(ii) The solid will displace water equal to its own volume, which is $large 450;cm^{3}$ . So, it will displace $large 450;cm^{3}$ of water.

Density of water is $large 1;g;cm^{-3}$ . Hence, from the formula,

$large Density;of;water=frac{Mass;of;water}{Volume;of;water}$

$large Mass;of;water=Density;of;watertimes Volume;of;water$

i.e. $large m=dtimes V$

$large =1times450$

= 450 g

Therefore, the mass of water displaced is 450 g.

(iii) $large therefore$ $large Relative;density;of;solid=frac{Density;of;solid}{Density;of;water}$

$large =frac{1.33}{1}=1.33$

Therefore, the relative density of solid is 1.33.

(iV) Since, the relative density of this solid (1.33) is greater than that of water (1), therefore this solid is heavier than water and hence it will sink in water.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The relative density of a substance is the ratio of its density to that of _______________________.
A. Solution	B. Water	C. Liquid	D. None of these.
Right Option : B
View Explanation

Question : 2

A ship rises up as it enters the sea from a river because
A. Sea water is harder than river water		B. Density of sea water is lesser than that river water
C. large quantity of sea water pushes ship up		D. Density of sea water is greater than that river water
Right Option : D
View Explanation

Question : 3

The density of a body is 800 kg/m3. Will it sink or float when dipped in a bucket of water?
A. Float	B. Sink	C. Cant say	D. None of these
Right Option : A
View Explanation