Question

A solid weighs $32\,gf$ in air and $28.8\,gf$ in water. What is the relative density of the solid?

Answer 1

Hint: To solve this question, we will use the basic concept of relative density. we will find the relative density by simply substituting the given information in the formula to obtain the required solution. And relative density is the ratio of the density of a substance with respect to the density of the other standard substance.

Formula used:
${\text{R}}{\text{.D = }}\dfrac{{{W_1}}}{{{W_1} - {W_2}}} \times {\text{R}}{\text{.D of water}}$
Where, Solids weights in air is ${W_1}$ and Solids weights in air is ${W_2}$ .

Complete step by step answer:
According to the question,solids weights in air is, ${W_1} = 32gf$ and solids weights in water is, ${W_2} = 28.8\,gf$. We have to find the relative density of solid,
${\text{R}}{\text{.D = }}\dfrac{{{W_1}}}{{{W_1} - {W_2}}} \times {\text{R}}{\text{.D of water}}$
Now, substituting the values in above formula we will get,
${\text{R}}{\text{.D = }}\dfrac{{32}}{{32 - 28.8}} \times {\text{1}} \\
\therefore {\text{R}}{\text{.D = 10}} \\ $
Hence, the relative density of the solid is $10$.

Additional information: Factors which affect the relative density,
Air bubbles: A little bubble with a diameter of 1 mm can boost the concentration by 0.5 mg, whereas those with a diameter of 2 mm can increase the concentration by 4 mg. As a result, double-check that the solid object or sinker immersed in the liquid is free of air bubbles.
Solid matter sample: The amount of fluid within the pitcher of the glass will rise if a sample with a high volume immersed in the fluid is used.
Temperature: Temperature variations have little effect on solids; hence the accompanying density changes are irrelevant. The Archimedes Principle, on the other hand, takes temperature into account when estimating the density of a liquid or solid. Temperature variations have a bigger impact on liquids, causing density changes on the order of 0.1 to 1 per °C.

Note: Important point to remember is that in the final answer there is no unit, as relative density is a dimensionless quantity because the relative density is the ratio as in ratio both the units get cancelled in numerator and denominator. So relative density has no unit.Let’s take an example,
\[{\text{Density of the oil}} = 800kg{\text{ }}{m^{ - 3}}\]
\[\Rightarrow {\text{Density of the water}} = 1000kg{\text{ }}{m^{ - 3}}\]
So, the relative density of the oil with respect to water will be,
$R.D = \dfrac{{{\rho _{{\text{oil}}}}}}{{{\rho _{{\text{water}}}}}}$
$\Rightarrow R.D = \dfrac{{800kg{\text{ }}{m^{ - 3}}}}{{1000kg{\text{ }}{m^{ - 3}}}} \\
\Rightarrow R.D = 0.8 $
From the above explanation we can understand that there is no unit in relative density.