One litre of milk weight `1.032 kg`. If it contains butter fat (density`=800 kg m^(-3)`) to the extent of `4%` by volume, then the density of "skimmed milk" will be __ `kg m^(-3)`

Options

A. 1240
B. 1402
C. 1042
D. 2104

Answer

3

Explanation

Density of skimmed milk `=("Mass of skimmed milk")/("Volume of skimmed milk")`
Skimmed milk means fat-free milk. Thus
Mass of skimmed milk `= ((Mass of ),(milk))-((Mass of),(fat))`
Let's consider `1 m^(3)` of milk, i.e., `1000 L` milk. Since the butter fat is present in milk to the extent of `4%` by volume, volume of fat is `4%` of `1 m^(3)`, i.e., `0.04 m^(3)`.
Mass of `1 L milk =1.035 kg`
Mass of `1 m^(3) milk=((1.035 kg)/L)((1000 L)/(1 m^(3)))`
`=1035 kg`
Mass of fat in `1 m^(3)` milk `=volumexxdensity`
`=(0.04 m^(3))(875 kg m^(-3))`
`=35 kg`
Thus, mass of skimmed milk
`=(1035 kg)-(35 kg)`
`=1000 kg`
Volume of skimmed milk `=("volume of milk")-("volume of fat")`
`=(1 m^(3))-(0.04 m^(3))`
`=0.96 m^(3)`
Density of skimmed milk `=(1000 kg)/(0.96 m^(3))=1042 kg//m^(3)`