A log of wood of mass 120 Kg floats in water. The weight that can be put on the raft to make it just sink, should be (density of wood `= 600 Kg//m`)

Answer

To solve the problem, let's follow these steps:

### Step 1: Understand the problem
We have a log of wood with a mass of 120 kg that floats in water. We need to find out how much additional weight can be placed on the log before it sinks. The density of the wood is given as 600 kg/m³.

### Step 2: Calculate the volume of the wood
The volume of the wood can be calculated using the formula:
\[ \text{Volume} (V) = \frac{\text{Mass}}{\text{Density}} \]
Substituting the values:
\[ V = \frac{120 \, \text{kg}}{600 \, \text{kg/m}^3} = 0.2 \, \text{m}^3 \]

### Step 3: Calculate the buoyant force
The buoyant force (upthrust) acting on the log when it is floating is equal to the weight of the water displaced by the volume of the log. The density of water is 1000 kg/m³. Therefore, the buoyant force can be calculated as:
\[ \text{Buoyant Force} = \text{Density of Water} \times \text{Volume of Wood} \times g \]
\[ \text{Buoyant Force} = 1000 \, \text{kg/m}^3 \times 0.2 \, \text{m}^3 \times g = 200 \, \text{kg} \cdot g \]

### Step 4: Set up the equation for sinking
When the log is just about to sink, the total weight (weight of the log plus the additional weight) equals the buoyant force:
\[ \text{Weight of Wood} + \text{Additional Weight} = \text{Buoyant Force} \]
Let the additional weight be \( m \):
\[ 120 \, \text{kg} \cdot g + m \cdot g = 200 \, \text{kg} \cdot g \]

### Step 5: Solve for the additional weight
Cancel \( g \) from both sides:
\[ 120 \, \text{kg} + m = 200 \, \text{kg} \]
Now, solve for \( m \):
\[ m = 200 \, \text{kg} - 120 \, \text{kg} = 80 \, \text{kg} \]

### Final Answer
The weight that can be put on the raft to make it just sink is **80 kg**.

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