Question

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

Answer 1

Hint: In the question, they've given us the mass of an empty bucket and its volume capacity. To find the mass of the bucket once it is filled with some liquid, we need to find the mass of the liquid when it occupies a volume of 20 liters. For this, we can use the given relative density and find it. Later, we can add the mass of an empty bucket and the liquid to have the mass of the filled bucket.

Formula used:
$mass = density \times volume$
$density = sp.gr \times 1000kg/{m^3}$

Complete answer:
The volume capacity of the bucket is given to be 20 liters. The liquid which is used to fill the bucket will have the same volume as 20 liters. Then the mass of the liquid will be given by
$density = \dfrac{{mass}}{{volume}} \Rightarrow mass = density \times volume$
We have the volume of liquid to be 20 liters and the density of the liquid will be
$\eqalign{
  & density = sp.gr \times 1000kg/{m^3} \cr
  & \Rightarrow density = 0.9 \times 1000kg/{m^3} \cr
  & \Rightarrow density = 900kg/{m^3} \cr} $
Substituting these quantities in the above formula, we will have
$\eqalign{
  & mass = density \times volume \cr
  & \Rightarrow mass = 900kg/{m^3} \times 20lts \cr
  & \Rightarrow mass = 900kg/{m^3} \times 20 \times {10^{ - 3}}{m^3} \cr
  & \Rightarrow mass = 18kg \cr} $
Therefore, the mass of the liquid occupying 20 liters is 18kg.
The total mass of the filled bucket will be the sum of the mass of liquid and mass of an empty bucket, which is $18kg + 1.5kg = 19.5kg$.
Thus, the mass of the bucket once it is filled with a liquid of specific gravity 0.9 is 19.5kg.

Note:
In the problem, we have converted the units of volume from liters to m$^3$, their relation is given by $1lt = {10^{ - 3}}{m^3}$. You must always pay attention to the units to avoid errors in calculation. The specific gravity, also called relative density is the ratio of the density of a substance to the density of water.