Question

A piece of solid weighs 120g in air, 80g in water and 60kg in a liquid. The relative density of the solid and that of the liquid are respectively.
A) \[2,\dfrac{1}{2}\]
B) \[2,\dfrac{3}{2}\]
C) \[3,\dfrac{1}{2}\]
D) \[3,\dfrac{3}{2}\]

Answer 1

Hint: Relative density- It is the ratio of density of the substance to the density of water at \[4^\circ C\].
i.e. \[RD = \dfrac{{{\text{Density of substance}}}}{{{\text{Density of water at }}{{\text{4}}^\circ}C}}\]
Where, RD denotes relative density. It is a pure ratio and has no units.

Complete step by step answer:
Given:
Weight of the air = 120g
Weight in water = 80g
Weight in liquid = 60kg
According to question:
We know that relative density of solid is given by:-
\[\Rightarrow RD = \dfrac{{W{t_{(air)}}}}{{W{t_{(air)}} - W{t_{(water)}}}}\]
\[\Rightarrow \dfrac{{120}}{{120 - 80}}\]
\[ \Rightarrow \dfrac{{120}}{{40}} = 3\]
Now, Relative density of liquid is
\[\Rightarrow RD = \dfrac{{W{t_{(air)}} - W{t_{(liquid)}}}}{{W{t_{(air)}} - W{t_{(water)}}}}\]
\[ \Rightarrow \dfrac{{120 - 60}}{{120 - 80}}\]
\[ \Rightarrow \dfrac{{60}}{{40}}\]
\[ \Rightarrow \dfrac{3}{2}\]
So, the relative density of the solid and that of the liquid are 3 and 3/2 respectively.

Hence, Option (D) is the correct answer.

Note: Relative density (RD) is also referred to as specific gravity. In the formula of relative density we take the density of water at 4 degree temperature because the density of water maximum at 4 degree C and which is equal to $1g/cm^3$ in CGS. Therefore, numerically the Relative density RD and density of substance are equal. In SI units, the density of water at 4 degree Celsius is $1000kg/m^3$.
Specific gravity or relative gravity of a substance will give us the idea about the relative mass of a substance. If the relative density or specific gravity of a substance is less than 1 then it will float and sink if its value is greater than 1.
Several liquids with different specific gravities:-

Material	Relative density (RD)
Lamp oil	0.8
Water	1
Milk	1.03
Honey	1.42

Relative density has major applications in determination of relative density in the petroleum industry where the products obtained are basically based on the measurements of their relative densities under the processing period. This is very important to us to provide data which is required for the conversion of kinematic viscosities to their dynamic viscosities.