A solid floats in a liquid in a partially dipped position.

Options

A. the solid exerts a force equal to its weight on the liquid
B. the liquid exerts a force of buoyancy on the solid which is equal to the weight of the solid
C. the weight of the displaced liquid equals the weights of the solid
D. the weight of the dipped part of the solid is equal to the weight of the displaced liquid

Answer

To solve the problem of a solid floating in a liquid in a partially dipped position, we can analyze the situation step by step using the principles of buoyancy and Archimedes' principle.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A solid object is floating in a liquid, with part of it submerged and part of it above the liquid surface. This indicates that the solid is in equilibrium.

2. **Applying Archimedes' Principle**:
- According to Archimedes' principle, a body that is partially or fully immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the body.

3. **Defining Forces**:
- Let \( F \) be the buoyant force acting on the solid.
- The weight of the solid is denoted as \( mg \), where \( m \) is the mass of the solid and \( g \) is the acceleration due to gravity.

4. **Equilibrium Condition**:
- For the solid to float in equilibrium, the upward buoyant force \( F \) must equal the downward gravitational force \( mg \).
- Therefore, we can write the equation:
\[ F = mg \]

5. **Relating Buoyant Force to Displaced Liquid**:
- The buoyant force \( F \) can also be expressed as the weight of the displaced liquid:
\[ F = \rho_w \cdot g \cdot V_d \]
- Here, \( \rho_w \) is the density of the liquid (water in this case), \( g \) is the gravitational acceleration, and \( V_d \) is the volume of the liquid displaced by the submerged part of the solid.

6. **Equating Forces**:
- Since both expressions for the buoyant force are equal, we can equate them:
\[ mg = \rho_w \cdot g \cdot V_d \]
- By simplifying, we find that:
\[ m = \rho_w \cdot V_d \]

7. **Analyzing the Options**:
- **Option 1**: The solid exerts a force equal to its weight on the liquid. (True)
- **Option 2**: The liquid exerts a force of buoyancy on the solid, which is equal to the weight of the solid. (True)
- **Option 3**: The weight of the displaced liquid equals the weight of the solid. (True)
- **Option 4**: The weight of the dipped part of the solid is equal to the weight of the displaced liquid. (False)

### Conclusion:
- Options 1, 2, and 3 are correct, while option 4 is incorrect.