The vessels A and B of equal volume and weight are immersed in water to depth h.The vessel A has an opening at the bottom through which water can enter.If the work done in immersing A and B are `W_(A)` and `W_(B)` respectively,then

Options

A. `W_(A)=W_(B)`
B. `W_(A)ltW_(B)`
C. `W_(AgtW_(B)`
D. None of these

Explanation

To solve the problem, we need to analyze the work done in immersing the two vessels A and B in water to a depth \( h \).

### Step-by-Step Solution:

1. **Understanding the Setup**:
- Both vessels A and B have equal volume and weight.
- Vessel A has an opening at the bottom, allowing water to enter, while vessel B is closed.

2. **Weight Considerations**:
- When vessel A is immersed, water enters through the opening, increasing its weight.
- Vessel B remains closed, so its weight does not change when immersed.

3. **Forces Acting on the Vessels**:
- The weight of vessel A increases as it fills with water, while the weight of vessel B remains constant.
- The buoyant force acting on both vessels is equal to the weight of the water displaced, which is the same for both vessels since they are of equal volume.

4. **External Force Required**:
- To sink vessel A, the external force \( F_A \) must overcome the buoyant force and the weight of the water inside it.
- For vessel B, the external force \( F_B \) must only overcome the buoyant force and its own weight.

5. **Comparison of Forces**:
- Since vessel A gains additional weight from the water entering it, the external force \( F_A \) required to immerse it is less than the external force \( F_B \) required for vessel B.
- Therefore, we have \( F_A < F_B \).

6. **Work Done Calculation**:
- Work done is defined as the force applied multiplied by the distance moved in the direction of the force.
- For vessel A, the work done \( W_A \) is given by:
\[ W_A = F_A \cdot h \]
- For vessel B, the work done \( W_B \) is given by:
\[ W_B = F_B \cdot h \]

7. **Conclusion**:
- Since \( F_A < F_B \), it follows that:
\[ W_A < W_B \]
- Hence, the work done in immersing vessel A is less than the work done in immersing vessel B.

### Final Result:
\[ W_A < W_B \]