Question

water has a density of 1gcm-3 and condensed milk has a density of 1.5gcm.A milk man mixed 100cm3 of water in 400cm-3.what is the density of milk mixed with water

Answer 1

Water has a density of $1\mathrm{gcm}^{-3}$ and condensed milk has a density of $1.5\mathrm{gcm}^{-3}$. A milk man mixed $100\mathrm{cm}^3$ of water in $400\mathrm{cm}^{-3}$. What is the density of milk mixed with water?

**Solution.**

$$\rho_w = 1 \frac{g}{cm^3}, \rho_m = 1.5 \frac{g}{cm^3}, V_m = 100cm^3V_w = 400cm^3;$$ $$\rho -?$$

The density of milk mixed with water is:

$$\rho = \frac{m}{V}.$$

The mass of the milk mixed with water is:

$$m = m_m + m_w.$$

The mass of the milk is:

$$m_m = \rho_m V_m.$$

The mass of the water is:

$$m_w = \rho_w V_w.$$

The volume of the milk mixed with water is:

$$V = V_m + V_w;$$

$V_m$ - the volume of the milk;

$V_w$ - the volume of the water.

The density of milk mixed with water is:

$$\rho = \frac{m_m + m_w}{V_m + V_w};$$ $$\rho = \frac{\rho_m V_m + \rho_w V_w}{V_m + V_w}.$$ $$\rho = \frac{1.5 \frac{g}{cm^3} 100cm^3 + 1 \frac{g}{cm^3} 400cm^3}{100cm^3 + 400cm^3} = 1.1 \frac{g}{cm^3}.$$

**Answer:** The density of milk mixed with water is $\rho = 1.1\frac{g}{cm^3}$.