One litre of milk weighs. `1.035 kg`. The butter fat is `4%(v//v)` of milk has density of `875 kg//m^(3)`. Find the density of fat free skimed milk.

Explanation

To find the density of fat-free skimmed milk, we can follow these steps:

### Step 1: Determine the mass of butter fat in 1 liter of milk
Given that the butter fat is 4% (v/v) of milk, we can calculate the volume of fat in 1 liter of milk.

\[ \text{Volume of fat} = 4\% \text{ of } 1 \text{ L} = \frac{4}{100} \times 1000 \text{ mL} = 40 \text{ mL} \]

### Step 2: Calculate the mass of butter fat
We know the density of butter fat is 875 kg/m³. To convert this to grams per mL:

\[ \text{Density of fat} = 875 \text{ kg/m}^3 = 0.875 \text{ g/mL} \]

Now, we can calculate the mass of the butter fat:

\[ \text{Mass of fat} = \text{Volume of fat} \times \text{Density of fat} = 40 \text{ mL} \times 0.875 \text{ g/mL} = 35 \text{ g} \]

### Step 3: Calculate the mass of fat-free skimmed milk
The total mass of 1 liter of milk is given as 1.035 kg, which is equivalent to 1035 g. Therefore, the mass of fat-free skimmed milk can be calculated as:

\[ \text{Mass of fat-free milk} = \text{Total mass of milk} - \text{Mass of fat} = 1035 \text{ g} - 35 \text{ g} = 1000 \text{ g} \]

### Step 4: Calculate the volume of fat-free skimmed milk
Since we have 40 mL of fat in the original 1 liter of milk, the volume of fat-free skimmed milk is:

\[ \text{Volume of fat-free milk} = 1000 \text{ mL} - 40 \text{ mL} = 960 \text{ mL} \]

### Step 5: Calculate the density of fat-free skimmed milk
Density is defined as mass divided by volume. Thus, we can find the density of fat-free skimmed milk:

\[ \text{Density of fat-free milk} = \frac{\text{Mass of fat-free milk}}{\text{Volume of fat-free milk}} = \frac{1000 \text{ g}}{960 \text{ mL}} \approx 1.04167 \text{ g/mL} \]

### Final Answer
The density of fat-free skimmed milk is approximately **1.04167 g/mL**.

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