Equal masses of water and a liquid of density 2g/cm3 are mixed together. The density of mixture is:

Options

A. (a)`2/3 g//c c`
B. (b)`4/3 g//c c`
C. (c)`3/2 g//c c`
D. (d)`3 g//c c`

Answer

To find the density of a mixture of equal masses of water and a liquid with a density of 2 g/cm³, we can follow these steps:

### Step 1: Define the given quantities
- Let the mass of water be \( m \).
- The density of water \( \rho_w = 1 \, \text{g/cm}^3 \).
- The density of the liquid \( \rho_l = 2 \, \text{g/cm}^3 \).

### Step 2: Calculate the volume of water
The volume of water can be calculated using the formula:
\[ V_w = \frac{m}{\rho_w} \]
Substituting the values:
\[ V_w = \frac{m}{1} = m \, \text{cm}^3 \]

### Step 3: Calculate the volume of the liquid
The volume of the liquid can be calculated using the formula:
\[ V_l = \frac{m}{\rho_l} \]
Substituting the values:
\[ V_l = \frac{m}{2} \, \text{cm}^3 \]

### Step 4: Calculate the total volume of the mixture
The total volume \( V_{total} \) of the mixture is the sum of the volumes of water and the liquid:
\[ V_{total} = V_w + V_l = m + \frac{m}{2} \]
To simplify:
\[ V_{total} = m + 0.5m = \frac{3m}{2} \, \text{cm}^3 \]

### Step 5: Calculate the total mass of the mixture
The total mass \( M_{total} \) of the mixture is the sum of the masses of water and the liquid:
\[ M_{total} = m + m = 2m \]

### Step 6: Calculate the density of the mixture
The density of the mixture \( \rho_{mix} \) can be calculated using the formula:
\[ \rho_{mix} = \frac{M_{total}}{V_{total}} \]
Substituting the values:
\[ \rho_{mix} = \frac{2m}{\frac{3m}{2}} = \frac{2m \cdot 2}{3m} = \frac{4}{3} \, \text{g/cm}^3 \]

### Conclusion
Thus, the density of the mixture is:
\[ \rho_{mix} = \frac{4}{3} \, \text{g/cm}^3 \]