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# An empty relative density bottle weighs 26.4 g. When fully filled with water its weight is 38.4 g, when filled with another liquid its weight is 35.4 g. Find the relative density of the liquid.${\text{A}}{\text{.}}$ 0.25${\text{B}}{\text{.}}$ 0.75${\text{C}}{\text{.}}$ 0.15${\text{D}}{\text{.}}$ 1

Last updated date: 16th Sep 2024
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- Hint- Here, we will proceed by finding the volume of the bottle which is equal to the volume of the water used to fill the bottle which is further equal to the volume of the liquid. Then, we will apply the formula i.e., Relative density of any liquid = $\dfrac{{{\text{Density of that liquid}}}}{{{\text{Density of water}}}}$.

Complete step-by-step solution -

Given, Mass of empty relative density bottle = 26.4 g
Mass of fully filled (with water) bottle = 38.4 g
Mass of fully filled (with another liquid) = 35.4 g
As we know that the mass of the water with which the bottle was filled can be obtained by subtracting the mass of empty relative density fully filled (with water) bottle from the mass of fully filled (with water) bottle.
i.e., Mass of water = Mass of fully filled (with water) bottle - Mass of empty relative density bottle
$\Rightarrow$Mass of water = 38.4 – 26.4 = 12 g
Since, density of water = 1 $\dfrac{{{\text{kg}}}}{{{{\text{m}}^3}}}$ = 1 $\dfrac{{\text{g}}}{{{\text{c}}{{\text{m}}^3}}}$
As, Density = $\dfrac{{{\text{Mass}}}}{{{\text{Volume}}}}{\text{ }} \to {\text{(1)}}$
Using the above formula, we can write
Volume of the water = $\dfrac{{{\text{Mass of water}}}}{{{\text{Density of water}}}} = \dfrac{{12}}{1} = 12{\text{ c}}{{\text{m}}^3}$
Since, the bottle is fully filled with water, the volume of the bottle will be equal to the volume of the water with which the bottle is filled.
So, Volume of the bottle = Volume of the water = 12 ${\text{c}}{{\text{m}}^3}$
Also we know that the mass of the liquid (other than water) with which the bottle was filled can be obtained by subtracting the mass of the empty relative density bottle from the mass of the fully filled (with liquid other than water) bottle.
i.e., Mass of water = Mass of fully filled (with liquid other than water) bottle - Mass of empty relative density bottle
$\Rightarrow$Mass of liquid (other than water) = 35.4 – 26.4 = 9 g
Also, with this liquid also the bottle is to be fully filled
So, Volume of liquid (other than water) = Volume of the bottle = 12 ${\text{c}}{{\text{m}}^3}$
Using formula given by equation (1), we have
Density of liquid (other than water) = $\dfrac{{{\text{Mass of liquid (other than water)}}}}{{{\text{Volume of liquid (other than water)}}}} = \dfrac{9}{{12}} = \dfrac{3}{4}{\text{ }}\dfrac{{\text{g}}}{{{\text{c}}{{\text{m}}^3}}}$
As, Relative density of any liquid = $\dfrac{{{\text{Density of that liquid}}}}{{{\text{Density of water}}}}$
Using the above formula, we can write
Relative density of the liquid (other than water) = $\dfrac{{{\text{Density of liquid }}\left( {{\text{other than water}}} \right)}}{{{\text{Density of water}}}} = \dfrac{{\left( {\dfrac{3}{4}} \right)}}{1} = \dfrac{3}{4} = 0.75$
Therefore, the relative density of the liquid other than water is 0.75
Hence, option B is correct.

Note- For any liquid, the relative density is the ratio of the density of that liquid to the density of water. This will give a dimensionless number (i.e., having no units). For any gas, the relative density is the ratio of the density of that gas to the density of air because for liquids, water is the reference and for gases, air is the reference.