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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

If a sample of metal weight 210 g in air, 180 g in water, 120 g in a liquid:
A. RD of metal is 3	B. RD of metal is 7	C. RD of liquid is 7	D. RD of liquid is (1/3)
Right Option : A
View Explanation

Question : 2

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

Question : 3

When an object of weight W is immersed in a liquid, its weight in the liquid is found to be $large W_1$ . When it is immersed in water, the weight of the water displaced is found to be $large W_2$ . The relative density of the liquid is _________________
A. $frac{W_2}{W_1}$	B. $frac{W-W_1}{W_2}$	C. $frac{W_2}{W-W_1}$	D. $frac{W-W_2}{W_1}$
Right Option : B
View Explanation

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