A raft of wood (density`=600kg//m^(3))` of mass `120 kg` floats in water. How much weight can be put on the raft to make it just sink?

Explanation

To solve the problem of how much weight can be put on the raft to make it just sink, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Density of the wood (raft) = 600 kg/m³
- Mass of the raft = 120 kg
- Density of water = 1000 kg/m³

2. **Calculate the Volume of the Raft**:
- The volume of the raft can be calculated using the formula:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{120 \text{ kg}}{600 \text{ kg/m}^3} = 0.2 \text{ m}^3 \]

3. **Determine the Total Weight When the Raft is Just Sinking**:
- When the raft is just about to sink, the weight of the raft plus any additional weight (let's denote this additional weight as \( W \)) will equal the buoyant force.
- The buoyant force can be calculated using Archimedes' principle:
\[ \text{Buoyant Force} = \text{Volume of displaced water} \times \text{Density of water} \times g \]
- Since the raft has a volume of 0.2 m³, the buoyant force is:
\[ \text{Buoyant Force} = 0.2 \text{ m}^3 \times 1000 \text{ kg/m}^3 \times g = 200 \text{ kg} \times g \]

4. **Set Up the Equation for Equilibrium**:
- At the point of sinking, the total downward force (weight of the raft + additional weight) equals the upward buoyant force:
\[ 120 \text{ kg} \times g + W = 200 \text{ kg} \times g \]

5. **Solve for the Additional Weight \( W \)**:
- Rearranging the equation gives:
\[ W = (200 \text{ kg} - 120 \text{ kg}) \times g \]
- Therefore:
\[ W = 80 \text{ kg} \times g \]

6. **Conclusion**:
- The weight that can be put on the raft to make it just sink is **80 kg**.