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 can follow these steps:

### Step-by-Step Solution:

1. **Understanding Apparent Weight**:
The apparent weight of a body submerged in a fluid is defined as the net downward force acting on the body. This is influenced by the actual weight of the body and the buoyant force acting on it.

2. **Define Actual Weight**:
The actual weight (W) of the object can be expressed as:
\[ W = mg \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity.

3. **Calculate Buoyant Force**:
The buoyant force (F_b) acting on the object when it is submerged in a fluid is given by Archimedes' principle:
\[ F_b = \rho_{\text{liquid}} \cdot V \cdot g \]
where \( \rho_{\text{liquid}} \) is the density of the liquid, \( V \) is the volume of the object, and \( g \) is the acceleration due to gravity.

4. **Relate Mass and Volume**:
The mass of the object can also be expressed in terms of its density:
\[ m = \rho_{\text{object}} \cdot V \]
where \( \rho_{\text{object}} \) is the density of the object.

5. **Express Apparent Weight**:
The apparent weight (W_a) can be calculated as:
\[ W_a = W - F_b \]
Substituting the expressions for weight and buoyant force, we have:
\[ W_a = mg - \rho_{\text{liquid}} \cdot V \cdot g \]

6. **Substituting Mass**:
Replace \( m \) with \( \rho_{\text{object}} \cdot V \):
\[ W_a = (\rho_{\text{object}} \cdot V \cdot g) - (\rho_{\text{liquid}} \cdot V \cdot g) \]
Factoring out \( Vg \):
\[ W_a = Vg (\rho_{\text{object}} - \rho_{\text{liquid}}) \]

7. **Analyzing Conditions**:
- If \( \rho_{\text{object}} > \rho_{\text{liquid}} \): The object sinks, and \( W_a > 0 \) (apparent weight is positive).
- If \( \rho_{\text{object}} < \rho_{\text{liquid}} \): The object floats, and \( W_a < 0 \) (apparent weight is negative).
- If \( \rho_{\text{object}} = \rho_{\text{liquid}} \): The object is neutrally buoyant, and \( W_a = 0 \) (apparent weight is zero).

### Conclusion:
The apparent weight of a body submerged in a fluid can be positive, negative, or zero depending on the relationship between the density of the object and the density of the fluid.