Large number of stones are placed in a small boat. The boat is floating in a water tank. If stones are unloaded in the water in the tank then which of the following are incorrect.

Options

A. Level of water will fall
B. Level of water will rise
C. Water level falls at first and then rises
D. Water level remains unchanged

Answer

To solve the problem, we need to analyze the situation step by step, focusing on the effects of unloading stones from the boat into the water tank.

### Step-by-Step Solution:

1. **Understand the Initial Situation**:
- A boat is floating in a water tank with a large number of stones placed in it. The boat is in equilibrium, meaning the buoyant force acting on it is equal to the total weight of the boat plus the stones.

2. **Identify the Forces**:
- The buoyant force (Fb) acting on the boat can be expressed as:
\[ Fb = V_{submerged} \times \rho_{water} \times g \]
- Here, \(V_{submerged}\) is the volume of the boat submerged in water, \(\rho_{water}\) is the density of water, and \(g\) is the acceleration due to gravity.

3. **Unloading Stones**:
- When stones are unloaded from the boat into the water, the weight of the stones is no longer supported by the boat. Instead, the stones displace an amount of water equal to their own volume when submerged.

4. **Effect on Buoyant Force**:
- Initially, the buoyant force is balancing the weight of both the boat and the stones. After unloading the stones:
- The buoyant force will now only balance the weight of the boat.
- The stones will exert a buoyant force equal to the volume of water they displace when submerged.

5. **Determine the Change in Water Level**:
- When the stones are in the boat, they cause the boat to displace a volume of water equal to their weight. When they are thrown into the water, they displace a volume of water equal to their own volume.
- Since stones are denser than water, the volume of water displaced by the stones when they are in the boat is greater than the volume of water displaced when they are submerged in water.

6. **Conclusion on Water Level**:
- Therefore, when the stones are unloaded, the overall volume of water displaced decreases, leading to a fall in the water level in the tank.

### Summary of Incorrect Statements:
- The water level will fall: **Correct**
- The water level will rise: **Incorrect**
- The water level will fall at first and then rise: **Incorrect**
- The water level remains unchanged: **Incorrect**

### Final Answer:
The incorrect statements are:
- The water level will rise.
- The water level will fall at first and then rise.
- The water level remains unchanged.