Question

Equal masses of water and a liquid of density \[2\] are mixed together, then the mixture has a density of
A. \[\dfrac{2}{3}\]
B. \[\dfrac{4}{3}\]
C. \[\dfrac{3}{2}\]
D. \[3\]

Answer 1

Hint: We can find the solution to the above question by using the density formula. We already know the density of one liquid. Also, we know that the density of water is equal to \[1g/c{m^3}\].

Complete step by step solution:
We can take the volume of the water to be \[{V_w}\] and the volume of the liquid to be \[{V_l}\]
We can also take the density of the water to be \[{\rho _w}\] and the density of the liquid to be \[{\rho _l}\].
The formula for the density is given as,
Density=mass/volume
\[\rho = \dfrac{m}{v}\]
Since it is given as both the water and the liquid as the same mass, we can take the mass to be \[2m\] for both water and liquid.
Now, Volume of water \[{V_w}\] =\[\dfrac{m}{{{\rho _w}}}\]
We know that the density of the water is equal to \[1g/c{m^3}\]
Substituting in the above equation,
\[{V_w}\]=\[\dfrac{m}{1}\]……… (1)
The volume of the liquid is\[{V_l}\]=\[\dfrac{m}{{{\rho _l}}}\]
Given that the density of the liquid is\[2\]
So,\[{V_l}\]=\[\dfrac{m}{2}\]……… (2)
Adding the volume of water and liquid=\[m + \dfrac{m}{2}\]=\[\dfrac{{3m}}{2}\]
Mass of both water and liquid is \[2m\]
Density=\[\dfrac{{2m}}{{3m}} \times 2\]=\[\dfrac{4}{3}\]
Therefore the correct option is B.

Note:
Density is defined as the mass of a unit volume of a material substance. Earth’s density is \[5.51g/c{m^3}\]. Density offers a convenient means of obtaining the mass of a body from its volume or vice versa.
Note that the density of water that we have taken in the above example is in \[g/c{m^3}\]. But if we take it in \[kg/{m^3}\] then it will be equal to \[997kg/{m^3}\].