A shpere of iron and another of wood, both of same radius are placed on the surface of water. State which of the two will sink? Give reason to your answer.

Answer

To determine which sphere will sink when placed in water, we need to analyze the densities of the materials involved and apply Archimedes' principle.

### Step-by-Step Solution:

1. **Identify the Materials and Their Densities**:
- We have two spheres: one made of iron and the other made of wood.
- The density of iron is significantly greater than the density of water (approximately 7.87 g/cm³ for iron vs. 1 g/cm³ for water).
- The density of wood is less than the density of water (typically around 0.5 to 0.9 g/cm³ for most types of wood).

2. **Apply Archimedes' Principle**:
- According to Archimedes' principle, an object submerged in a fluid experiences an upward force (upthrust) equal to the weight of the fluid displaced by the object.
- For an object to float, the weight of the object must be equal to the upthrust. If the weight of the object is greater than the upthrust, the object will sink.

3. **Analyze the Iron Sphere**:
- The weight of the iron sphere (W_iron) is greater than the upthrust (U_iron) acting on it because the density of iron is greater than that of water.
- Therefore, W_iron > U_iron, which means the iron sphere will sink.

4. **Analyze the Wooden Sphere**:
- The weight of the wooden sphere (W_wood) is less than the upthrust (U_wood) acting on it because the density of wood is less than that of water.
- Therefore, W_wood < U_wood, which means the wooden sphere will float.

5. **Conclusion**:
- The iron sphere will sink because its density is greater than that of water, while the wooden sphere will float because its density is less than that of water.

### Final Answer:
The iron sphere will sink, while the wooden sphere will float.

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