Question

An empty density bottle of 30 g, when filled completely with water, weighs 62 g. When filled completely with another liquid, its mass is 54 g. Calculate the density of the liquid.

• A.
  $1.33gc{m}^{-3}$
• B.
  $0.75gc{m}^{-3}$
• C.
  $0.8gc{m}^{-3}$
• D.
  $0.65gc{m}^{-3}$

Answer 1

The correct option is B

$0.75gc{m}^{-3}$
Given,
Mass of empty density bottle = 30 g
Mass of density bottle filled with water = 62 g
Mass of density bottle filled with the liquid = 54 g
Mass of water = 62 - 30 = 32 g
Now, the density of water = $1gc{m}^{-3}$

$Volumeofwater=\frac{Massofwater}{Densityofwater}$
$Volumeofwater=\frac{32g}{1gc{m}^{-3}}$
Volume of water = $32c{m}^3$

Volume of water = Volume of density bottle = $32c{m}^3$

Mass of liquid only = 54 g - 30 g = 24 g

$Densityofliquid=\frac{Massofliquid}{Volumeofliquid}$
= $\frac{24g}{32c{m}^3}$

$=0.75gc{m}^{-3}$
Thus, the density of unknown liquid is $0.75gc{m}^{-3}$