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A small bottle weighs $20\,g$ when empty and $22\,g$ when filled with water.When it is filled with oil it weighs $21.76\,g$. What is the density of oil?

Last updated date: 22nd Jul 2024
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Hint:Since water is denser (heavier) than oil, they cannot blend. Oil floats on the surface of the water. Oil can still float on top of water because it is less solid than water, resulting in an oily surface layer. After a hard shower, certain water puddles will have a layer of oil floating on them, as you might have seen on the sidewalks.

Complete step by step answer:
The density of a matter is its mass per unit volume (more specifically, its volumetric mass density; also known as real mass). While the Latin letter D can also be used, the symbol for density is (the lowercase Greek letter $ρ$ rho). Density is classified mathematically as mass divided by volume.
\[\rho = \dfrac{m}{V}\]
where the density is $ρ$, the mass is $m$, and the volume is $V$. In certain contexts (for example, in the oil and gas industry in the United States), density is arbitrarily interpreted as its weight per unit volume, which is technically incorrect; this amount is more precisely known as specific weight.

Here, weight of water = weight of filled glass− weight of empty bottle =$22\,g – 20\,g = 2\,g$
Weight of oil = $21.76\,g−20\,g = 1.76\,g$
\[{\text{ Relative density of oil }} = \dfrac{{{\text{ density of oil }}}}{{{\text{ density of water }}}} \\
\Rightarrow {\text{ Relative density of oil }}= \dfrac{{\dfrac{{{\text{ mass of oil }}}}{{{\text{ Volume }}}}}}{{\dfrac{{{\text{ mass of water }}}}{{{\text{ Volume }}}}}}\]
\[\Rightarrow {\text{ Relative density of oil }}= \dfrac{{1.76}}{2} \\
\therefore {\text{ Relative density of oil }} = 0.88\]

Note:The dimensionless quantity "relative mass" or "specific gravity," i.e. the ratio of the object's density to that of a reference material, generally water, is often used to simplify density comparisons between various systems of units. As a result, if the relative density of a material is less than one, it floats in water.