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`)

Options

A. `80Kg`
B. `50Kg`
C. `60 Kg`
D. `30Kg`

Answer

To solve the problem of how much weight can be added to a floating log of wood to make it just sink, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Mass of the log of wood, \( m_{\text{wood}} = 120 \, \text{kg} \)
- Density of the wood, \( \rho_{\text{wood}} = 600 \, \text{kg/m}^3 \)

2. **Calculate the Volume of the Log:**
- The volume \( V \) of the log can be calculated using the formula:
\[ V = \frac{m_{\text{wood}}}{\rho_{\text{wood}}} \]
- Substituting the values:
\[ V = \frac{120 \, \text{kg}}{600 \, \text{kg/m}^3} = 0.2 \, \text{m}^3 \]

3. **Determine the Weight of the Log:**
- The weight \( W_{\text{wood}} \) of the log is given by:
\[ W_{\text{wood}} = m_{\text{wood}} \cdot g \]
- Where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). However, we can keep it in terms of mass since we will compare forces later.

4. **Calculate the Buoyant Force:**
- The buoyant force \( F_b \) acting on the log when it is floating is equal to the weight of the water displaced by the volume of the log:
\[ F_b = \rho_{\text{water}} \cdot V \cdot g \]
- The density of water \( \rho_{\text{water}} = 1000 \, \text{kg/m}^3 \). Thus:
\[ F_b = 1000 \, \text{kg/m}^3 \cdot 0.2 \, \text{m}^3 \cdot g = 200 \, \text{kg} \cdot g \]

5. **Set Up the Equilibrium Condition:**
- For the log to just sink, the total weight (weight of the log plus the additional weight \( m \)) must equal the buoyant force:
\[ W_{\text{wood}} + W_{\text{additional}} = F_b \]
- In terms of mass:
\[ 120 \, \text{kg} + m = 200 \, \text{kg} \]

6. **Solve for the Additional Mass \( m \):**
- Rearranging the equation gives:
\[ m = 200 \, \text{kg} - 120 \, \text{kg} = 80 \, \text{kg} \]

7. **Conclusion:**
- The weight that can be put on the log to make it just sink is \( 80 \, \text{kg} \).

### Final Answer:
The weight that can be added to the log to make it just sink is **80 kg**.

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