- Step 1: Calculate Effective Water Retained in Soil:
$$\text{Applied Volume} = 650\text{ m}^3$$
$$\text{Losses} = 10\% \implies \text{Retained Volume} = 650 \times 0.90 = 585\text{ m}^3$$
$$\text{Mass of Retained Water} = 585\text{ m}^3 \times 1000\text{ kg/m}^3 = 585,000\text{ kg}$$
- Step 2: Calculate Mass of Dry Soil in Root Zone:
$$\text{Soil Volume} = \text{Area} \times \text{Depth} = 1000\text{ m}^2 \times 1.8\text{ m} = 1800\text{ m}^3$$
$$\text{Dry Soil Mass} = 1800\text{ m}^3 \times 1450\text{ kg/m}^3 = 2,610,000\text{ kg}$$
- Step 3: Calculate Moisture Content Increase ($\Delta m$):
$$\Delta m = \frac{585,000}{2,610,000} \times 100 = 22.41\% \approx 22.4\%$$
- Step 4: Calculate Field Capacity ($FC$):
$$FC = \text{Existing Moisture} + \Delta m = 8.0\% + 22.4\% = 30.4\%$$
- Conclusion: The field capacity of the soil is 30.4%. (Correct answer: Option 3)
