Question

A tank of 5 m height is half filled with water and then filled to the top with oil of density 0.85 g
cc, then the density of the total mixture is

a) 0.925 x 10° kg/m'
b) 0.925 x 10 kg/m
c) 1 x 10 kg/m
d) 1.925 x 10 kg/m​

Answer 1

Concept

• Density = $\dfrac{mass}{volume}$

Solution

Let the volume of the tank be 2V so that the volume of water and oil will be V and V respectively.

We know, density of water = 1 g/cc.

mass of water in the tank = density x volume

                                          = 1 x V = V

mass of oil in the tank =  0.85 x V = 0.85V

Total mass = V + 0.85V = 1.85V

Hence, density = $\dfrac{1.85V}{2V} \\ \\ \\ =\: 0.925\:g\:cm^{-3}$

Thus, the density of the solution is $0.925\times 10^3\:kg\:m^{-3}$.

Answer 2

Concept

Density = $\dfrac{mass}{volume}$

Solution

Let the volume of the tank be 2V so that the volume of water and oil will be V and V respectively.

We know, density of water = 1 g/cc.

mass of water in the tank = density x volume

                                          = 1 x V = V

mass of oil in the tank =  0.85 x V = 0.85V

Total mass = V + 0.85V = 1.85V

Hence, density = $\dfrac{1.85V}{2V} \\ \\ \\ =\: 0.925\:g\:cm^{-3}$

Thus, the density of the solution is $0.925\times 10^3\:kg\:m^{-3}$.