Question

The mass of an empty bucket of capacity 20 litres is 1.5 kg. Find the mass of the bucket when completely filled with a liquid of relative density of 0.9.

Answer 1

Hint: The relative density of the liquid is proportional to the density of that liquid and is inversely proportional to the density of the water. As the density of the water at \[4{}^\circ C\] is constant, thus, one of the parameters can be found if another parameter is given.

Formula used:
\[R.D=\dfrac{{{d}_{l}}}{{{d}_{w}}}\]
\[d=\dfrac{m}{V}\]

Complete step by step answer:
From given, we have the data,
The mass of an empty bucket, m = 1.5 kg
The capacity of an empty bucket, V = 20 litres
The relative density of the liquid, R.D = 0.9
Firstly, compute the density of the liquid.
The relative density is given by the formula,
Relative density = density of the liquid / density of the water at \[4{}^\circ C\]
\[R.D=\dfrac{{{d}_{l}}}{{{d}_{w}}}\]
The density of the water at \[4{}^\circ C\]is \[1000{kg}/{{{m}^{3}}}\;\].
Substitute the values in the above equation to find the density of the liquid.
\[\begin{align}
  & 0.9=\dfrac{{{d}_{l}}}{1000{kg}/{{{m}^{3}}}\;} \\
 & {{d}_{l}}=0.9\times 1000{kg}/{{{m}^{3}}}\; \\
 & {{d}_{l}}=900{kg}/{{{m}^{3}}}\; \\
\end{align}\]
The capacity of the bucket is given in terms of litres.
\[\begin{align}
  & 1\,litre=0.001{{m}^{3}} \\
 & 20litres=20\times 0.001{{m}^{3}} \\
 & 20litres=0.02{{m}^{3}} \\
 & \Rightarrow V=0.02{{m}^{3}} \\
\end{align}\]
Now compute the mass of the liquid.
The density of the liquid is given by the formula,
\[\begin{align}
  & d=\dfrac{m}{V} \\
 & m=d\times V \\
\end{align}\]
Substitute the given values in the above equation to find the mass of the liquid.
\[\begin{align}
  & m=900{kg}/{{{m}^{3}}}\;\times 0.02{{m}^{3}} \\
 & m=18kg \\
\end{align}\]
Now compute the total mass of the bucket when completely filled with a liquid.
The total mass of the bucket = The mass of an empty bucket + The mass of the liquid present in the bucket.
The total mass of the bucket \[=1.5kg+18kg\]
The total mass of the bucket \[=19.5kg\]

The mass of the bucket when completely filled with a liquid of relative density of 0.9 is 19.5 kg.

Note:
The things to be on your finger-tips for further information on solving these types of problems are: Always take into consideration the unit of the volume and that of the density.
The unit of the volume should be converted from litres to meters and the unit of the density should be converted from grams/milligrams to kilograms.