Question

$1L$ of milk weighs $1.035$ kg. The butter fat it contains to the extent of $4\%$ by volume has a density of $875kg/m^3.$ Find the density of the fat-free 'skimmed' milk.
($1m^3={10}^{3}L$)

• A. $942kg/m^3$
• B. $1124kg/m^3$
• C. $1042kg/m^3$
• D. $1242kg/m^3$

Answer 1

The correct option is C $1042kg/m^3$

Weight of $1m^3$ milk $=1.035\times {10}^3=1035kg$
Weight of the fat in $1m^3$ of milk $=0.04\times 875kg$
($1m^3$ milk contains $0.04m^3$ of fat) = 35 kg.
$\therefore \text{density of skimmed milk}=\frac{\text{wt. of skimmed milk}}{\text{vol. of skimmed milk}}$
$=\frac{(1035-35)kg}{(1-0.04)m^3}=1042kg/m^3$