The apparent weight of a body

Options

A. may be positive
B. may be negative
C. may be zero
D. is always positive

Answer

To solve the problem regarding the apparent weight of a body submerged in a fluid, we will analyze the forces acting on the body and determine the conditions under which the apparent weight can be positive, negative, or zero.

### Step-by-Step Solution:

1. **Understanding Apparent Weight**:
- Apparent weight is defined as the net force acting on a body when it is submerged in a fluid. It is calculated as the actual weight of the body minus the buoyant force acting on it.
- Mathematically, it can be expressed as:
\[ W_{apparent} = W_{actual} - F_{buoyant} \]
where \( W_{actual} \) is the weight of the body and \( F_{buoyant} \) is the buoyant force.

2. **Identifying Forces**:
- The actual weight \( W_{actual} \) of the body acts downward due to gravity.
- The buoyant force \( F_{buoyant} \) acts upward and is equal to the weight of the fluid displaced by the body (Archimedes' principle).

3. **Case 1: Body Floating on the Surface**:
- When the body is floating, the buoyant force equals the weight of the body:
\[ F_{buoyant} = W_{actual} \]
- Therefore, the apparent weight is:
\[ W_{apparent} = W_{actual} - W_{actual} = 0 \]
- **Conclusion**: Apparent weight is zero when the body is floating.

4. **Case 2: Body Rising in the Fluid**:
- If the body is moving upward in the fluid, the buoyant force is greater than the weight of the body:
\[ F_{buoyant} > W_{actual} \]
- Thus, the apparent weight becomes:
\[ W_{apparent} = W_{actual} - F_{buoyant} < 0 \]
- **Conclusion**: Apparent weight is negative when the body is rising.

5. **Case 3: Body Sinking in the Fluid**:
- If the body is sinking, the weight of the body is greater than the buoyant force:
\[ W_{actual} > F_{buoyant} \]
- Therefore, the apparent weight is:
\[ W_{apparent} = W_{actual} - F_{buoyant} > 0 \]
- **Conclusion**: Apparent weight is positive when the body is sinking.

6. **Final Conclusion**:
- The apparent weight of a body submerged in a fluid can be:
- Zero when floating,
- Negative when rising,
- Positive when sinking.

### Summary of Options:
- **Option 1**: Apparent weight can be positive (when sinking).
- **Option 2**: Apparent weight can be negative (when rising).
- **Option 3**: Apparent weight can be zero (when floating).
- **Option 4**: This option is incorrect as it states otherwise.