The total weight of a piece of wood is 6 kg in the floating state in water its 1/3 part remains inside the water on this floating solid what maximum weight is to be put such that the whole of the piece of wood is to be drowned in the water

Options

A. 12 kg
B. 10 kg
C. 14 kg
D. 15 kg

Answer

To solve the problem step by step, we will analyze the situation of the floating piece of wood and determine the maximum weight that can be added to it before it is completely submerged in water.

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- The total weight of the piece of wood (Wb) is given as 6 kg.
- In the floating state, 1/3 of the wood is submerged in water.

2. **Calculating the Buoyant Force**:
- The buoyant force (F_thrust) acting on the wood when it is floating can be calculated using Archimedes' principle.
- Since 1/3 of the wood is submerged, the buoyant force is equal to the weight of the water displaced by the submerged part of the wood.
- Therefore, the buoyant force can be expressed as:
\[ F_{thrust} = \text{Weight of the submerged part} = \frac{1}{3} W_b = \frac{1}{3} \times 6 \text{ kg} = 2 \text{ kg} \]

3. **Setting Up the Equation for Maximum Weight**:
- When an additional weight (mg) is added to the wood, the total weight acting downwards becomes:
\[ W_{total} = W_b + mg \]
- For the wood to be completely submerged, the total weight must equal the buoyant force when the wood is fully submerged. The buoyant force when fully submerged is equal to the weight of the entire volume of water displaced by the wood.
- Since the wood is 3 times the weight of the submerged part, we have:
\[ F_{thrust} = 3 \times W_b = 3 \times 6 \text{ kg} = 18 \text{ kg} \]

4. **Equating Forces**:
- Setting the total weight equal to the buoyant force gives us:
\[ W_b + mg = F_{thrust} \]
\[ 6 \text{ kg} + mg = 18 \text{ kg} \]

5. **Solving for the Maximum Additional Weight**:
- Rearranging the equation to find mg:
\[ mg = 18 \text{ kg} - 6 \text{ kg} = 12 \text{ kg} \]

6. **Conclusion**:
- The maximum weight that can be added to the piece of wood before it is completely submerged is 12 kg.

### Final Answer:
The maximum weight that can be added is **12 kg**.

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